摘要
时滞现象、不确定性参数扰动和随机因素广泛存在于各类实际系统中,常常会导致系统性能降低甚至不稳定.因此,在系统建模时,需要考虑时滞现象,不确定性参数扰动以及随机因素等对系统的影响.目前,对于随机时滞系统控制理论方面的研究己取得了丰富的成果,但与确定性时滞系统较完善的研究成果相比,还有很多有待解决的问题.
本学位论文应用Lyapunov-Krasovskii泛函方法,以线性矩阵不等式为工具,研究了几类随机时滞系统的稳定性,鲁棒控制与滤波问题,提出了针对随机时滞系统新的分析和综合方法,获得了一些研究成果.本文主要工作有以下几个方面：
1.研究了不确定中立型随机分布时滞系统的鲁棒混合H2/H∞保性能控制问题.通过构造Lyapunov-Krasovskii泛函(LKF),应用It6微分公式,交叉项定界方法,Jensen不等式,线性矩阵不等式(linear matrix inequality,简写为LMI)等方法,建立了随机有界实引理,给出了鲁棒混合H2/H∞保性能控制器存在的时滞相关的充分条件,设计出鲁棒混合H2/H∞保性能控制器,利用Gronwall-Bellman不等式,证明了闭环系统在无干扰输入和满足不确定容许条件下的均方指数稳定性,系统中的时滞为时变时滞,包括中立项时滞、离散时滞和分布时滞,并且讨论了三者相等和不等两种情形.并通过数值例子说明结果的有效性和验证H2、H∞性能指标.
2.通过构造LKF和引入自由权矩阵,应用It6微分公式,LMI方法,交叉项定界方法,Jensen不等式等方法.研究了不确定随机时滞系统和不确定中立型随机分布时滞系统的鲁棒H2/H∞保性能滤波问题.根据Hamilton-Jacoby-Issac条件,利用配方法,建立了不确定随机时滞系统的有界实引理,得到了鲁棒H2/H∞保性能滤波器存在的时滞相关的充分条件,设计出鲁棒H2/H∞保性能滤波器,使得在无干扰输入情况下,对于所有容许不确定性,滤波误差系统依概率全局渐近稳定；建立了不确定中立型随机分布时滞系统的有界实引理,得到了鲁棒H2/H∞保性能滤波器存在的时滞相关的充分条件,设计出鲁棒H2/H∞指数滤波器,使得在无干扰输入情况下,对于所有容许不确定性,该系统均方指数稳定.所考虑的时滞为区间时变时滞,并且去掉了时滞导数上界小于1的限制条件,所构造LKF充分考虑了有关时变时滞,时滞上下界的信息以及它们之间的关系.数值例子说明了结果的有效性.
3.应用Lyapunov-Krasovskii泛函方法和LMI方法方法,研究了不确定中立型随机分布时滞系统和不确定中立型随机时滞系统的时滞相关均方指数稳定性问题.运用自由权矩阵方法,交叉项定界方法,Jensen不等式等方法,得到了不确定中立型随机分布时滞系统时滞相关均方指数稳定的充分条件,数值例子显示所得结果改进了部分现有成果；运用广义Finsler引理(generalized Finsler lemma,简写为GFL),得到了不确定中立型随机时滞系统时滞相关均方指数稳定的充分条件,避免使用模型变换方法,自由权矩阵方法,Jensen不等式,不仅减少了保守性,而且降低了计算复杂程度,数值例子说明了方法的有效性,显示所得结果改进了相关文献的结果.所考虑的时滞为区间时变时滞,并且去掉了时滞导数上界小于1的限制条件,所构造LKF充分考虑了有关时变时滞,时滞上下界的信息以及它们之间的关系.
4.研究了具有非线性项的不确定随机Markovian跳跃时滞系统的鲁棒H∞动态输出反馈控制和滤波问题,非线性项包括满足范数有界条件的非线性系数不确定性和满足Lipchiz线性增长条件的非线性随机扰动项,时滞为模态依赖的区间时变时滞,并且去掉了时滞导数上界小于1的保守性条件.应用LKF方法,广义Finsler引理,LMI等方法,得到了这类系统均方指数稳定的时滞相关充分条件,并进行了L2性能分析.针对这类系统的鲁棒H∞动态输出反馈控制和滤波问题,分别建立了随机有界实引理,分别通过求解联立LMIs,设计了鲁棒H∞动态输出反馈控制器和鲁棒H∞滤波器,使得在无干扰输入情况下,对于所有容许不确定性和非线性项,闭环系统和滤波误差系统是均方指数稳定的.避免了使用模型变换方法,自由权矩阵方法,不仅降低了保守性,而且提高了计算效率.构造LKF时,充分考虑了有关时变时滞,时滞上下界的信息以及它们之间的关系.数值例子说明了所使用方法的低保守性,简便性和结果的有效性.
5.研究了一般非线性随机时滞系统的鲁棒H2/H∞全局线性化滤波问题.一般非线性随机时滞系统的非线性比滤波问题,可以通过求解二阶Hamilton-Jacoby不等式(HJI)来获得,但是一般情况下,二阶HJI是难以求解的.本文通过把一般非线性随机时滞系统等价地改写为有限个线性随机时滞系统的凸组合加上近似误差来表示,在全局线性化框架下,针对得到的等价系统,考虑鲁棒H2/H∞全局线性化滤波问题,应用Lyapunov-Krasovskii泛函方法,Jensen不等式,LMI方法,根据Hamilton-Jacoby-Issac条件,结合配方法,建立了随机有界实引理,基于该有界实引理,通过求解联立LMIs,设计鲁棒H2/H∞全局线性化滤波器,使得滤波误差系统在无干扰输入情况下依概率全局渐近稳定.给出数值例子来说明方法的有效性和设计程序.
最后,对全文进行总结,并提出了今后需要继续研究的方向.
It is well known that time-delays, parameter uncertainties and stochastic perturbation are frequently encountered in various practical and engineering fields. These factors are usually the source of instability and degradation in control systems. Therefore, one has to consider the effect of time-delays, parameter uncertainties and stochastic perturbation when modeling the systems. Plentiful results have been reported on control theory for stochastic delayed system, however, there remain many open but challenging problems.
Based on the knowledge of stochastic analysis and Lyapunov-Krasovskii functional the-ory, by linear matrix inequality technique etc., this thesis focuses on stability analysis, robust control and filtering problem for several kinds of stochastic time-delay systems. The main results obtained in this thesis are as follows:
1. The problem of robust mixed H2/H∞guaranteed-cost control for uncertain neu-tral stochastic distributed time-delay systems (UNSDDS) is investigated. By Ito formulation, cross-terms bounding technique, Jensen inequality, Gronwall-Bellman inequality and LMI ap-proach etc., Lyapunov-Krasovskii functionals are constructed to establish a linear stochastic bounded real lemma, by which delay-dependent conditions for the solvability of the robust mixed H2/H∞guaranteed-cost control problem are proposed, and the robust mixed H2/H∞guaranteed-cost controllers are designed to guarantee the loop systems are mean-square expo-nentially stable for all admissible uncertainties with zero disturbance input. The time-varying delays considered include neutral delay, discrete delay and distributed delay, which may be equal to each other or not. Numerical examples are presented to show the effectiveness of the results and very the H2、H∞performances.
2. By Ito formulation, cross-terms bounding technique, Jensen inequality, Gronwall-Bellman inequality and LMI approach etc., Lyapunov-Krasovskii functionals are construct-ed and free-weighting matrices are introduced to study robust H2/H∞filtering problems for uncertain stochastic time-delay systems (USDS) and uncertain neutral stochastic distributed time-delay systems. According to Hamilton-Jacoby-Issac condition, complete square method is applied to derive linear stochastic bounded real lemmas for uncertain stochastic time-delay systems, by which delay-dependent conditions for the solvability of the robust H2/H∞filter-ing problems are proposed, and the robust H2/H∞filters are designed to guarantee the filtering error systems are globally asymptotically stable in probability for all admissible uncertainties with zero disturbance input. Based on linear stochastic bounded real lemmas for uncertain s-tochastic time-delay systems established for uncertain neutral stochastic distributed time-delay systems, delay-dependent conditions for the solvability of the robust H2/H∞filtering problems are proposed, and the robust H2/H∞filters are designed to guarantee the filtering error systems are mean-square exponentially stable for all admissible uncertainties with zero disturbance in-put. The delays considered are interval time-varying, and the restriction that the upper bound of the delay derivative is less than1is removed by introducing free-weighting matrices. The new Lyapunov-Krasovskii functional takes into account the information of the time-varying delay, the upper and lower bounds of the time-varying delay. Numerical examples are given to illustrate the effectiveness of the results.
3. The delay-dependent mean-square exponential stability problems of uncertain neu-tral stochastic distributed time-delay systems and uncertain stochastic time-delay systems are investigated. By Ito formulation, cross-terms bounding technique, Jensen inequality, Gronwall-Bellman inequality and LMI approach etc., Lyapunov-Krasovskii functionals are constructed and free-weighting matrices are introduced to obtain delay-dependent mean-square exponential stability condition for uncertain neutral stochastic distributed time-delay systems. Numerical examples are proposed to show that the results improve some existing ones. By Lyapunov-Krasovskii theory and LMI method, under the generalized Finsler lemma (GFL) framework, delay-dependent mean-square exponential stability criteria are established without involving any model transformation, Jensen inequality or additional free-weighting matrix. Moreover, GFL is also employed to obtain stability criteria for a class of uncertain linear stochastic neu-tral systems with different discrete and neutral delays. Numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones. The delays considered are interval time-varying, and the restriction that the upper bound of the delay derivative is less than1is removed by introducing free-weighting matrices or applying GFL. The new Lyapunov-Krasovskii functional takes into account the information of the time-varying delay, the upper and lower bounds of the time-varying delay.
4. The problems of robust H∞dynamic output feedback control and filtering for uncer-tain I to-type stochastic Markovian jump systems with unknown nonlinearities satisfying lin-ear Lipchiz growth condition and interval mode-dependent time-varying delays is investigated. The aim of this problem is to design a Markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean-square stable for a prescribed H∞disturbance attenuation level. By Lyapunov-Krasovskii theory and generalized Finsler lemma (GFL), novel delay-range-dependent and delay-derivative-dependent sufficient conditions are obtained to guarantee the existence of desired exponential Hx filter, which can be constructed by solving simultaneous Linear matrix inequalities (LMIs). Neither model transformations nor free-weighting matrices are involved, therefore, conservatism and computation burden result from them can be avoided. Furthermore, the usual assumption that the derivatives of the time-varying delays are less than1is removed due to the applying of GFL. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.
5. The robust mixed H2/H∞global linearization filtering problem for a general nonlin-ear stochastic system with interval time-varying delay and exogenous disturbance is studied. For a general nonlinear stochastic system with exogenous disturbance, although the robust H∞filter can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality (HJI), it is difficult to solve the second-order nonlinear HJI except those special cases. Based on the global linearization scheme and Lyapunov-Krasovskii functional theory, a stochastic bounded real lemma is established, by which the robust H∞global linearization filter design for the non-linear stochastic time-varying delay system is proposed via solving simultaneous linear matrix inequalities (LMIs) associated with the filtering problem in linear stochastic time-varying delay systems at vertices instead of solving the HJI associated with the H∞filtering problem in the nonlinear stochastic time-varying delay system. When the worst case disturbance attenuation of H∞filtering is considered, the mixed H2/H∞filter design problem is also solved from the H2suboptimal estimation point of view. A simulation example is provided to illustrate the effectiveness of the proposed method.
Finally, the conclusions are summarized and the directions of future studies are proposed.
引文
[1]刘永清,邓飞其.随机系统的变结构控制[M].广州：华南理工大学出版社,1998.
[2]岳东,彭晨,韩清龙.网络控制系统的分析与综合[M].北京：科学出版社,2007.
[3]Kolmanovskii V. B., Myshkis A.D., Applied Theory of Functional Differential Equation-s[M]. Dordrecht:Kluwer Academic Publishers,1992.
[4]Gu KQ, Kharitonov VL, Chen J. Stability of time-delay systems[M]. Birkhauser:Boston, MA,2003.
[5]F. Black and M.Seholes. The Pricing of options and corporate liabilities[J].J. Politic. E-con.,81:637-654,1973.
[6]R. Z. Has'minskii, Stochastic Stability of Differential Equations[M]. Alphen aan den, The Netherlands:Sijtjoff and Noordhoff,1980.
[7]Friedman A. Stochastic Differential Applications[M]. Academic Press, Volumn 1,1975, Volumn2,1983.
[8]龚光鲁.随机微分方程引论[M].北京：北京大学出版社,1987.
[9]龚光鲁,钱敏平.应用随机过程教程一及在算法和智能计算中的随机模型[M].北京：清华大学出版社,2004.
[10]E. Gershon, U. Shaked, and I. Yaesh. H∞ Control and Estimation of State-Multiplicative Linear. Systems. Berlin, Germany:Springer,2005.
[11]Mao XR. Stochastic Differential Equations and Applications[M]. Horwood:Chi chester, 2008.
[12]秦元勋,王慕秋,王联.运动稳定性理论及应用[M].北京：科学出版社,1980.
[13]黄琳.稳定性与鲁棒性的理论基础[M].北京：科学出版社,2003
[14]王康宁.最优控制的数学理论[M],北京：国防工业出版社,1995.
[15]X.M. Zhang, M. Wu, J.H. She, and Y. He. Delay-dependent stabilization of linear systems with time-varying state and input delays[J]. Automatica,41:1405-1412,2005.
[16]Y. He, M. Wu, J. She, and G. Liu. Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems & Control Letters,51:57-65,2004.
[17]Y. He, Q. Wang, L. Xie, et. al, Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control, vol.52, no.2, pp.293-299,2007.
[18]X.M. Zhang and Q.L. Han. Robust H∞ filtering for a class of uncertain linear systems with time-varying delay[J]. Automatica,44:157-166,2008.
[19]高会军.基于参数依赖Lyapunov函数的不确定动态系统的分析与综合[D].哈尔滨：哈尔滨工业大学博士论文,2005.
[20]吴敏,何勇.时滞系统鲁棒控制-自由权矩阵方法[M].北京：科学出版社,2008.
[21]Mori T., Kokame H.Stability of x(t)= Ax(t)+Bx(t-τ)[J].IEEE Transactions on Automatic Control,1989,34:460-462.
[22]Brierley S., Chiasson J., Lee E. etc., On stability independent of delay for linear system-s[J]. IEEE Transactions on Automatic Contro,1982,27:252-254.
[23]秦元勋,刘永清,王联,郑祖麻.带有时滞的动力系统的运动稳定性[M].科学出版社,1989.
[24]廖晓听.稳定性的数学理论及应用[M].武汉：华中师范大学出版社,2001.
[25]K. Gu, An integral inequality in the stability problem of time-delay systems[A]. in Pro-ceedings of 39th IEEE Conference on Decision and Control[C], vol.3, pp.2805-2810, Sydney, Austrilia, December 2000.
[26]E. Fridman, U. Shaked, Delay-dependent stability and H∞ control:constant and time-varying delays[J].International Journal of Control,2003,76:48-60.
[27]Park P. A delay-dependent stability criterion for systems with uncertain time-invariant delays[J].IEEE Transactions on Automatic Control,1999,44:876-877.
[28]Moon Y. S., Park P., Kwon W.H., etc. Delay-dependent robust stabilization of uncertain state-delayed systems[J].International Journal of Control,2001,74:1447-1455.
[29]E. Fridman, New Lyapunov-Krasovskii functional for stability of linear retarded and neu-tral type systems[J].System & Control Letters,2001,43:309-319.
[30]K. Gu, S.I. Nieuleseu, Further remarks on additional dynamics in various model trans-formations of linear delay systems[J]. IEEE Transactions on Automatic Control,2001, 46(3):497-500.
[31]O.M. Kwon, J. H. Park, S.M. Lee On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays [J], Applied Mathematics and Computation 203 (2008) 843-853.
[32]张先明.基于积分不等式方法的时滞相关鲁棒控制研究[D].长沙：中南大学博士论文,2006.
[33]何勇.基于自由权矩阵的时滞相关鲁棒稳定与镇定[D].长沙：中南大学博士论文,2004.
[34]M.Wu, Y. He, and J.H.She. New delay-dependent stability criteria for an stabilizing meth-ods for neutral systems[J]. IEEE Trans.Automa. Control,49(12):2266-2271,2004.
[35]S. Xu and J.Lam. Improved delay-dependent stability criteria for time-delay systems[J]. IEEE Trans.Automa. Control,50(3):384-387,2005.
[36]Y. He, Q. Wang, C. Lin, et. al., Delay-range-dependent stability for systems with time-varying delay[J]. Automatica, vol.43, no.2, pp.371-376,2007.
[37]X. F. Jiang and Q. L. Han, Delay-dependent robust stability for uncertain linear systems with interval time-varying delay[J]. Automatica, vol.42, no.6, no.1059-1065,2006.
[38]S. Xu and J. Lam, On equivalence and efficiency of certain stability criteria for time-delay systems[J], IEEE Transactions on Automatic Control 52(1)(2007) 95-101.
[39]Yue D., Robust stabilization of uncertain systems with unknown input delay[J], Au-tomatiea,2004,40(2):331-336.
[40]Yue D., Han Q.L., Delayed feedback control of uncertain systems with time-varying input delay[J], Automatiea,2005,41(2):233-240.
[41]D. Yue, Q. L. Han and J. Lam, Network-based robust H∞ control of systems with uncer-tainty[J]. Automatica, vol.41, no.6, pp.999-1007,2005.
[42]Han Q.L., A discrete delay decomposition approach to stability of linear retarded and neutral systems[J], Automatiea,2009,45(2):517-524.
[43]Boyd S, Ghaoui L El, Feron E, et al. Linear Matrix Inequalities in System and Control Theory[J]. Philadelphia, PA:SIAM,1994.51-60
[44]V. Suplin, E. Fridman and U. Shaked, H∞ control of linear uncertain time delay systems-a projection approach[J]. IEEE Transactions on Automatic Control, vol.51, no.4, pp. 680-685,2006.
[45]X. M. Zhang, Q. L. Han. Stability analysis and H∞ filtering for delay differential systems of neutral type[J]. IET. Control Theory Appl.,1(3):749-755,2007.
[46]J. Qiu, G. Feng, J. Yang, A new design of delay-dependent robust H∞ filtering for discrete-time T-S fuzzy systems with time-varying delay[J], IEEE Transactions on Fuzzy Systems 17(5)(2009) 1044-1058.
[47]Y.S. Zhang, S.Y. Xu, and B.Y. Zhang. Robust Output Feedback Stabilization for Uncer-tain Discrete-Time Fuzzy Markovian Jump Systems With Time-Varying Delays [J], IEEE Transactions on Fuzzy Systems 17(2)(2009) 411-420.
[48]F.W. Yang, Y.M. Li, Set-Membership Filtering for Discrete-Time Systems With Nonlinear Equality Constraints[J], IEEE Transactions on Automatic Control 54(10) (2009) 2480-2486.
[49]W.W. Che and J.L. Wang, Static Output Feedback H∞ Control for Discrete-Time Markov Jump Linear Systems [A], in:Proceedings of 8th IEEE International Conference on Con-trol and Automation[C], Xiamen, China, June,2010, pp.2278-2283.
[50]V. Suplin, E. Fridman, and U. Shaked, H1 control of linear uncertain time-delay sys-tems-A projection approach[J]. in Proc.43rd IEEE Conf. Decision Control, Atlantis, Bahamas, Dec.2004, pp.4548-4553.
[51]S. Xu and J. Lam. A survey of linear matrix inequality techniques in stability analysis of delay systems[J]. Int. J. Systems Science, vol.39, no.12, pp.1095-1113,2008.
[52]Arnold L. Stochastic Differential Equations:Theory and Applications[M]. New York: Jokn Wiley & Sons,1974.
[53]胡宣达.随机微分方程稳定性理论[M].南京：南京大学出版社,1985.
[54]Chen H. F., Guo L. Identification and Stochastic Adaptive Control[M]. Birkhauser, Boston,1991.
[55]郭雷.时变随机系统-稳定性、控制与估计[M].长春：吉林科学技术出版社,1993.
[56]Mao X. R. Exponential Stability of Stochastic Dieffrential Equations[M]. New York, Ma-reelDekker,1994.
[57]王康宁.最优控制的数学理论[M],北京：国防工业出版社,1995.
[58]Deng H., Krstic M. Stochastic nonlinear stabilization-Ⅰ:A backstepping design[J]. Sys-tems Control Letter,1997,32:143-150.
[59]朱位秋.非线性随机动力学与控制-Hamilton理论体系框架[M].北京：科学出版社,2003.
[60]方洋旺,潘进.随机系统分析与应用[M].西北工业大学出版社,2006.
[61]沈轶,廖晓昕.随机时滞神经网络的指数稳定性[J].中国学术期刊科技快报,1998,1：120-125.
[62]Mao X. R., Marion G., Renshaw E. Environmental Brownian noise suppresses explosions in population dynamics[J]. Stochastic Processes and their Applieations,2002,97:95-110.
[63]Karoui EI Peng S. Quenez M. C. Backward stocin hastic differential equations finance[J]. Math. finance.,1997,7:1-71.
[64]Boukas E. K. Stabilization of stochastic singular nonlinear hybrid systems[J]. Nonlinear Analysis,2006,64:217-228.
[65]Luo J. W., Zou J. Z., Hou Z. T. Comparison Principle and stability criteria for stochas-tic differential delay equations with Makrovian switching[J]. Science in China-Series A, 2003,46(1):129-138.
[66]Yuan C., Mao X. R. Asymptotic stability in distribution of stochastic differential equations with Makrovian switching[J]. Stochastic Processes and Their Applications,2003,103: 277-291.
[67]Wu S. J., Han D. Exponential stability of functional differential systems with impulsive ef-fect on random moments[J]. Computer and Mathematics with Applications,2005,50:321-328.
[68]吴述金,韩东,付还宁.随机脉冲随机微分方程解的存在唯一性[J].数学学报,2008,51(6)：1041-1052.
[69]Charles R. D., Khachik V. S., Peter S. A numerical method for some stochastic differential equations with multiplicative noise[J]. Physics Letters A,2005,344:149-155.
[70]Mahmoud M. E., Khairia E. E., Osama L. M., etl. Numerical methods for some non-linear stochastic differential equations[J]. Applied Mathematics and Computation,2005, 168:65-75.
[71]Q.Y. Li, S.Q. Gan, Almost sure exponential stability of numerical solutions for stochastic delay differential equations with jumps[J], J. Appl. Math. Comput.,37(2011),541-557.
[72]Boukas E. K. Exponential stabilizability of stochastic systems with markovian jumping parameters[J]. Automatica,1999,35:1437-1441.
[73]Bao J. D., Deng F. Q., Luo Q. Robust stochastic stabilization of uncertain Markovian jumping systems with distributed time-delay Based on LMIs approach[A]. Proeeedings of the IEEE International Symposium on Intelligent Control[C], Houston, USA,2003.
[74]D. Yue, J. Fang, and S. Won. Delay-dependent robust stability of stochastic uncertain systems with time delay and Markovian jump parameters [J]. Circuits, Systems and Signal Processing,22(4):351-365,2003.
[75]S. Xu, J. Lam, X. Mao, and Y. Zou. A new LMI condition for delay dependent robust stability of stochastic time-delay systems[J]. Asian Journal of Control,7:419-423,2005.
[76]吴立刚,王常虹,高会军,曾庆双.时滞不确定随机系统基于参数依赖Lyapunov函数的稳定性条件[J].控制理论与应用,24(4)：607-612,2007.
[77]华民刚,邓飞其,彭云建.不确定变时滞随机系统的鲁棒均方指数稳定性[J].控制理论与应用,26(5)：558-561,2009.
[78]Y. Chen, A. Xue. An improved stability criterion for uncertain stochastic delay system-s with nonlinear uncertainties[J]. IET Control Theory & Applications,2(11):966-973, 2008.
[79]陈云.随机时滞系统的分析与综合[D].杭州：杭州电子科技大学博士学位论文,2008.
[80]陈云,薛安克,王俊宏.随机时滞系统的时滞相关无源控制[J].自动化学报35(3)：324-327,2009.
[81]R. Yang, P. Shi, H. Gao. New delay-dependent stability criterion for stochastic systems with time delays. IET Control Theory & Applications,11(2):966-973,2008.
[82]W.H. Chen, Z. H. Guan and X. Lu, Delay-dependent exponential stability of uncertain stochastic systems with multiple delays:an LMI approach[J]. Systems & Control Letters, vol.54, no.6, pp.547-555,2005.
[83]G. Chen and Y. Shen, Robust H∞ filter design for neutral stochastic uncertain systems with time-varying delay[J]. Journal of Mathematical Analysis and Applications, vol.353, no.1, pp.196-204,2009.
[84]Huang LR, Mao XR. Delay-Dependent Exponential Stability of Neutral Stochastic Delay Systems[J], IEEE Transactions on Automatic Control 2009; 54(9):147-152.
[85]Y. Zhang, Y. H and M. Wu, Delay-dependent robust stability for uncertain stochastic sys-tems with interval time-varying delay[J]. Acta Automatica Sinica, vol.35, no.5, pp.577-582,2009.
[86]宋博.中立型随机时滞系统鲁棒控制与滤波[D].南京：南京理工大学博士学位论文.2008年.
[87]Song B., Xu S., Zou Y, Delay-dependent robust H∞ filtering for uncertain neutral s-tochastic time-delay systems[J]. Circuits Systems Signal Process, vol.28, pp.241-256, 2009.
[88]B. Song, S. Xu, J. Xia, et. al., Design of robust non-fragile H∞ filters for uncertain neutral stochastic system with distributed delays[J]. Asian Journal of Control, vol.12, no.1, pp. 39-45,2010.
[89]X. D. Li, Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type[J]. Applied Mathematics and Computation, vol.215, no. 12, pp.4370-4384,2010.
[90]H. C. Yan, X. H. Huang, H. Zhang, et. al., Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay [J].Chaos, Solitons and Fractals, vol. 40, no.4, pp.1668-1679,2009.
[91]H. C. Yan, Max Q.-H. Meng, H. Zhang, et. al.,Robust H∞, exponential filtering for uncer-tain stochastic time-delay systems with Markovian switching and nonlinearities[J].Applied Mathematics and Computation, vol.215, no. xx, pp.4358-4369,2010.
[92]H. C. Yan, H. Zhang, H. B. Shi, et. al., Robust H∞ Filtering for Uncertain Nonlinear S-tochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters [J]. Circuits Syst Signal Process, vol.30, no. xx, pp.303-321,2011.
[93]陈贵词.中立型随机时滞系统的H∞控制与滤波器设计[D].武汉：华中科技大学博士学位论文.2010年.
[94]Y. Chen and W.X. Zheng, Stability and L2 Performance Analysis of Stochastic Delayed Neural Networks[J]. IEEE Transactions On Neural Networks, vol.22, no.10, pp.1662-1668,2011.
[95]Z. Yang, D. Xu, X. Li. Exponential P-stability of impulsive stochastic differential equa-tions with delays[J]. Phys. Lett. A,359:129-137,2006.
[96]L. G. Xu, D. Y. Xu. Exponential p-stability of impulsive stochastic neural networks with mixed delays[J]. Chaos, Solitons & Fractals,41(1):263-272,2008.
[97]J. Yang, S. M. Zhong, W.P Luo. Mean square stability analysis of impulsive stochastic differential equations with delays[J]. Journal of Comput. and Appl. Math.,216(2):474-483,2008.
[98]H. Zhang, Z. H. Guan. Stability analysis on uncertain stochastic impulsive systems with time-delay[J], Physics Letters A,372(39):6053-6059,2008.
[99]L. G. Xu, D. Y. Xu. Mean square exponential stability of impulsive control stochastic systems with time-varying delay[J], Physics Letters A,373:328-333,2009.
[100]S. W. Zhao, J. T. Sun, H. J. Wu. Stability of linear stochastic differential delay systems under impulsive control[J]. IET Control Theory Appl.,3(11):1547-1552,2009.
[101]G.H.Zhao, M.H.Song,M.Z.Liu. Exponential stability of Euler-Maruyama solutions for impulsive stochastic differential equations with delay[J]. Appl. Math.Comput.,215:3425-3432,2010.
[102]J. Yang, S. M. Zhong, W.P. Luo, and G.H. Li. Delay-dependent stabilization for stochas-tic delayed fuzzy systems with impulsive effects [J]. International Journal of Control, Au-tomation, and Systems,8(1):127-134,2010.
[103]W. H. Zhang, H. S. Zhang, B. S. Chen. Stochastic H2/H∞ control with (x, u,u)-dependent noise:Finite horizon case[J], Automatica,43(3):513-521,2007.
[104]Wu YH, Guan ZH. On dissipativity and stabilization of time-delay stochastic system-s with switching control[J], Nonlinear Analysis:Real World Applications 2011; 12(4): 2031-2039.
[105]He Y, Zhang Y, Wu M, Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-vary ing delay [J], International Journal of Robust and Nonlinear Control 2010;20(1):16-26. DOI:10.1002/rnc.1412
[106]Kwon OM. Stability criteria for uncertain stochastic dynamic systems with time-varying delays[J], International Journal of Robust and Nonlinear Control 2011; 21(3):338-350. DOI:10.1002/rnc.1600
[107]H.B. Gu, H.J. Jiang, Z. D. Teng, Mean square exponential stability in high-order s-tochastic impulsive neural networks with time-varying delays[J], J. Appl. Math. Comput., 1-2(2009),151-170.
[108]Wang Y Y, Xie L H, de Souza Carlos E. Robust control of a class of uncertain nonlinear systems, Syst Control Lett,1992,19:139-149
[109]Liu YR, Wang ZD, Liu XH. Robust H∞ control for a class of nonlinear stochastic sys-tems with mixed time delay[J], International Journal of Robust and Nonlinear Control 2007; 17(16):1525-1551.DOI:10.1002/rnc.1185
[110]Yang R.N., Gao H.J., Shi P., Delay-dependent robust H∞ control for uncertain stochas-tic time-delay systems[J], International Journal of Robust and Nonlinear Control 2010; 20(16):1852-1865.DOI:10.1002/rnc.1552
[111]Zhang J.H., Shi P., Qiu J.Q., Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems[J], Journal of The Franklin Institute 2009;346(7):676-690
[112]Chen Y, Xue AK, and Lu RQ. Robust H∞ guaranteed cost control for uncertain stochastic delayed systems[J], Acta Automatica Sinica 2008;34(8):900-906.
[113]Xu SY, Shi P, Chu YM, Zou Y. Robust stochastic stabilization and H∞ control of un-certain neutral stochastic time-delay systems[J], Journal of Mathematical Analysis and Applications 2006; 314:1-16.
[114]Qiu JQ, He HK, Shi P. Robust Stochastic Stabilization and H∞ Control for Neutral S-tochastic Systems with Distributed Delays[J], Circuits, Systems, and Signal Processing 2011; 30:287-301.
[115]Xu S., Chu Y., Lu J., et. al. Exponential Dynamic Output Feedback Controller Design for Stochastic Neutral Systems With Distributed Delays[J], IEEE Transactions on Systems, Man and Cybernetics, Part A:Systems and Humans 2006; 36(3):540-548.
[116]Berman N, Shaked U. H∞-like control for nonlinear stochastic systems[J], System and Control Letters 2006; 55(3):247-257.
[117]Senthilkumar T, Balasubramaniam P. Delay-dependent robust H∞ control for uncertain stochastic T-S fuzzy systems with time-varying state and input delays[J], International Journal of Systems Science 2011; 42(5):877-887.
[118]B. S. Chen and W. Zhang, Stochastic H2/H∞ control with state-dependent noise[J], IEEE Trans. Autom. Control, vol.49, pp.45-57,2004.
[119]Zhang WH, Zhang HS, Chen BS. Stochastic H2/H∞ control with dependent noise:Fi-nite horizon case[J], Automatica 2006; 42(11):1891-1898.
[120]Zhang W.H., Huang Y.L., Xie L.H., Infinite horizon stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noise[J], Automatica, 44(9),2306-2316(2008)
[121]Zhang WH, Feng G. Nonlinear stochastic H2/H∞ control with (x,u, v)-dependent noise: Infinite horizon case[J], IEEE Transactions on Automatic Control 2008;53(5):1323-1328.
[122]Hou T, Zhang WH, Ma HJ. Finite horizon H2/H∞ control for discrete-Time stochastic systems with Markovian jumps and multiplicative noise[J], IEEE Transactions on Auto-matic Control 2010; 55(5):1185-1191.
[123]Yang F, Wang ZD, Ho DWC. Robust mixed H2/H∞ for a class of nonlinear stochastic systems[J], IEE Proceeding Control Theory Application,2006; 153(2):175-184.
[124]H. R. Karimi, Robust Delay-Dependent H∞ Control of Uncertain Markovian Jump Sys-tems with Mixed Neutral, Discrete and Distributed Time-Delays[J], IEEE Trans. Circuits and Systems I,8(2011),1910-1923.
[125]H. R. Karimi et al, Robust mixed H2/H∞ delayed state-feedback control of neutral delay systems with time-varying delays[J]. Asian Journal of Control,5(2008),569-580.
[126]Hale J, Lunel S. Introduction to Functional Differential Equations[M]. Mewyork: Springer-Verlag,1993.
[127]Boukas E.K., Liu Z. Deterministic and Stochastic Time-Delay Systems[M]. Birkhauser: Boston,2002.
[128]S. Y. Xu and T. W. Chen, Robust H∞ control for uncertain stochastic systems with state delay[J]. IEEE Transactions on Automatic Control, vol.47, no.12, pp.2089-2094,2002.
[129]Gahinet P, Nemirovski A, Laub AJ, Chilali M. LMI Control Toolbox For use with Mat-lab[M]. The MATH Works Inc.:Natic, MA,1995.
[130]W. Mceneaney, Robust H∞ filtering for nonlinear systems[J], Syst. Control Lett.,33(5): 315-325,1998.
[131]C. Yung, Y. Li, and H. Sheu, H∞ filtering and solution bound for nonlinear systems[J], Int. J. Control,74(6):565-570,2001.
[132]K. Kiriakidis, H∞ optimal filters for a class of nonlinear models, in Proc. Amer. Control Conf.,2002:2336-2339.
[133]S. Xu and T. Chen, Robust H∞ filtering for uncertain stochastic time-delay systems[J], Asian J. of Control,5(3):364-373,2003.
[134]Y. Lin and J. Lo, Robust mixed filtering for time-delay fuz2y systems[J], IEEE Trans. Signal Process.54(8):2897-2909,2006.
[135]A. Elsayed, M.J. Grimble, A new approach to H∞ design of optimal digital linear filters, IMA Journal of Mathematical Control & Information, vol.6, no.2, pp.233-251,1989.
[136]K.M. Nagpal, P.P. Khargonekar, Filtering and smoothing in an H∞ setting[J]. Internati-nal Journal of Control, vol.36, no.1, pp.152-166,1991.
[137]C.E. De Souza, R.M. Palhares, P.L.D. Peres, Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays, IEEE Transactions on Signal Processing, vol.49, no.2, pp.569-576,2001.
[138]Z. Wang, D.P. Goodall, K.J. Burnham, On designing observers for time-delay systems with nonlinear disturbances [J]. Internatinal Journal of Control, vol.75, no.11, pp.803-811,2002.
[139]S. Xu, T. Chen, An LMI approach to the H∞ filter design for uncertain systems with distributed delays, IEEE Transactions on Circuits and Systems Ⅱ:Express Briefs, vol.51, no.4, pp.195-201,2004.
[140]D. Yue, Q.L. Han, Robust H∞ filter design of uncertain descriptor systems with discrete and distributed delays, IEEE Transactions on Signal Processing, vol.52, no.11,3200-3212,2004.
[141]H. J. Gao and C. H. Wang, A delay-dependent approach to robust H∞ filtering for uncer-tain discrete-time state-delayed systems[J]. IEEE Transactions on Signal Processing, vol. 52, no.6, pp.1631-1640,2004.
[142]E. Fridman, U. Shaked, An improved delay-dependent H∞ filtering of linear neutral systems, IEEE Transactions on Signal Processing, vol.52, no.3, pp.668-673,2004.
[143]E. Fridman, U. Shaked, L. Xie, Robust H∞ filtering of linear systems with time-varying delay[J]. IEEE Transactions on Automatic Control, vol.48, no.1,159-165,2003.
[144]S. Xu, J. Lam, T. Chen, Y. Zou, A delay-dependent approach to robust H∞ filtering for uncertain distributed delay systems[J]. IEEE Transactions on Signal Processing, vol.53, no.10, pp.3764-3772,2005.
[145]Z. Wang, J. Lam, X. Liu, Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances[J]. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, vol.51, no.5, pp.262-268,2004.
[146]W. H. Zhang, B.S. Chen, C.S. Tseng, Robust H∞ filtering for nonlinear stochastic sys-tems[J]. IEEE Transactions on Signal Processing, vol.53, no.2, pp.589-598,2005.
[147]Z. Wang, F. Yang, D.W.C. Ho, et. al., Robust H∞ filtering for stochastic time-delay systems with missing measurements[J]. IEEE Transactions on Signal Processing, vol.54, no.7, pp.2579-2587,2006.
[148]Z. Wang, Y. Liu, X. Liu, H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities[J]. Automatica, vol.44, no.5,1268-1277,2008.
[149]H. Liu, F. Sun, K. He, et. al., Design of reduced-order H∞ filter for Markovian jumping systems with time delay [J]. IEEE Transactions on Circuits and Systems Ⅱ:Express Briefs, vol.51, no.11, pp.607-612,2004.
[150]G. Wei, Z. Wang, H. Shu, et. al., A delay-dependent approach to H∞ filtering for s-tochastic delayed jumping systems with sensor non-linearities[J]. Internatinal Journal of Control, vol.80, no.6, pp.885-897,2007.
[151]Y. Liu, Z. Wang, X. Liu, Robust H∞ filtering for discrete nonlinear stochastic systems with time-varying delay, Journal of Mathematical Analysis and Applications, vol.341, no. 1, pp.318-336,2008.
[152]Y. Chen, W. X. Zheng and A. Xue, A new result on stability analysis for stochastic neutral systems[J]. Automatica, vol.46, no.12, pp.2100-2104,2010.
[153]Luo Q., Mao X., Shen Y., New criteria on exponential stability of neutral stochastic differential delay equations[J]. System & Control Letters vl.55, no.10, pp.826-834,2006
[154]W. Chen, W. Zheng and Y. Shen, Delay-dependent stochastic stability and H∞ control of uncertain neutral stochastic systems with time delay[J]. IEEE Transactions on Automatic and Control, vol.54, no.7, pp.1660-1667,2009.
[155]W. Feng and H. X. Wu, Global asymptotic stability analysis for stochastic neutral-type delayed neural networks[J]," in Proceedings of 2010 Chinese Control and Decision Con-ference, pp.2658-2662, Xuzhou, China, May 2010.
[156]H. Y. Shao, Improved delay-dependent stability criteria for systems with a delay varying in a range[J]. Automatica, vol.44, no.12, pp.3215-3218,2008.
[157]J. J. Yu, K. J. Zhang and S. M. Fei, Further results on mean square exponential stability of uncertain stochastic delayed neural networks [J]. Communications in Nonlinear Science and Numerical Simulation, vol.14, no.4, pp.1582-1589,2009.
[158]A. E. Rodkina and M. V. Basin, On delay-dependent stability for vector nonlinear s-tochastic delay-difference equations with Volterra diffusion term[J]. Systems & Control Letters, vol.56, no 4, pp.423-430,2007.
[159]M. V. Basin and A. E. Rodkina, On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays[J]. Nonlinear Analysis:Theory, Methods & Applications, vol.68, no.8, pp.2147-2157,2008.
[160]T. Li, A. G. Song, S. M. Fei, Robust stability of stochastic Cohen-Grossberg neural networks with mixed time-varying delays[J]. Neurocomputing, vol.73, no.1-3, pp.542-551,2009.
[161]C. X. Li, J. T. Sun, R. Y. Sun, Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects[J]. Journal of the Franklin Institute, vol.347, no.7, pp.1186-1198,2010.
[162]C. X. Li, J. P. Shi, J. T. Sun, Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks[J]. Nonlinear Analysis:Theory, Methods & Applications, vol.74, no.10, pp.3099-3111,2011.
[163]K. Q. Gu, Q. L. Han, A. C. J. Luo et. al., Discretized Lyapunov functional for system-s with distributed delay and piecewise constant coefficients [J]. International Journal of Control, vol.74, no.7, pp.737-744,2001.
[164]Y. Chen and W.X. Zheng, On Stability of Switched Time-Delay Systems Subject to Non-linear Stochastic Perturbations[A]. in:Proceedings of 49th IEEE Conference on Decision and Control[C], Atlanta, GA, USA, December,2010, pp.2644-2649.
[165]Haykin S. Neural networks[M].NJ:Prentice-Hall; 1994.
[166]Niculescu S. Delay effects on stability:a robust control approach[M]. New York: Springer; 2001.
[167]S. Xu, T. Chen, J. Lam, Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays[J]. IEEE Transactions on Automatic Control vol.48, no.5, pp.900-907,2003.
[168]S. Xu, J. Lam and X. Mao, Delay-Dependent H∞ Control and Filtering for Uncertain Markovian Jump Systems With Time-Vary ing Delays [J]. IEEE Transactions on Circuits and Systems Ⅰ:Regular Papers, vol.54, no.9, pp.2070-2077,2007.
[169]Wang G L. Partially mode-dependent design of H∞ filter for stochastic Markovian jump systems with mode-dependent time delays[J]. Journal of Mathematical Analysis and Ap-plications.2011,383:573-584
[170]Y. Chen, A. Xue, S. Zhou, et. al., Delay-dependent robust control for uncertain stochastic time-delay systems[J]. Circuits, Systems & Signal Processing, vol.27, pp.447-460,2008
[171]X.F.Liao, K.W.Wong, C.G.Li. Global exponential stability for a class of generalized neu-ral networks with distributed delays[J]. Nonlinear Anal:Real World Appl.,2004,15:527-547.
[172]X.F.Liao, C.D.Li. An LMI approach to asymptotical stability of multi-delayed neural networks[J]. Phys.D,2005,200(1-2):139-155.
[173]刘群.外部激励和惯性项对时滞神经网络动力学行为的影响研究[D].重庆：重庆大学博士学位论文.2008.
[174]W.H. Mao, F.Q. Deng, A.H. Wan. Robust mixed H2/H∞ guaranteed cost control of un-certain stochastic neutral systems[J]. Journal of Application & Informatics, Vol.30(2012), No.5-6, pp.699-717.
[175]W.H. Mao, F.Q. Deng, A.H. Wan. Robust mixed H2/H∞ filtering for uncertain stochas-tic systems with interval time-varying delays[A]. In:Proc 31th Chinese Control Confer-ence[C], Hefei,2012,1676-1683
[176]W.H. Mao, F.Q. Deng, A.H. Wan. Delay-dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-varying Delay [J]. Journal of Ap-plied Mathematics, Volume 2012, Article ID 593780,22 pages, doi:10.1155/2012/593780
[177]中野道雄著,吴敏译.重复控制[M].长沙：中南工业大学出版社,1995
[178]Kiriakidis K. H∞ optimal filters for a class of nonlinear models[A]. In:Proc Amer Con-trol Conf[C], Anchorage, AK,2002,2336-2339
[179]Seo J, Yu M J, Park C G, et al. An extended robust H∞ filter for nonlinear uncertain sys-tems with constraints[A]. In:Proc 44th IEEE Conf Decision Control/Eur Control Conf[C], Seville, Spain,2005,1935-1940
[180]Xu S Y, Lam J, Mao X R. Delay-dependent H∞ control and filtering for uncertain Marko-vian jump systems with time-varying delays[J]. IEEE Trans Circuits Syst I, Reg Papers, 2007,54:2070-2077
[181]Chen B S, Tsai C L, Chen Y F. Mixed H2/H∞ filtering design in multirate transmulti-plexer system:LMI approach[J]. IEEE Trans Signal Process,2001,49:2693-2701
[182]Gershon E, Limebeer D J N, Shaked U, et al. Robust H∞ filtering of stationary continuous-time linear systems with stochastic uncertainties[J]. IEEE Trans Autom Con-trol,2001,46:1788-1793
[183]Xu S Y, Chen T, Reduced-order H∞ filtering for stochastic system[J]. IEEE Trans Signal Process,2002,50:2998-3007
[184]Chen B S, Zhang W H. State feedback H∞ control of nonlinear stochastic systems[J]. SIAM J Control Optim,2006,44:1973-1991
[185]Chen B S, Zhang W H, Chen Y Y On the robust state estimation of nonlinear stochastic systems with state-dependent noise[C]. Proc. Int Conf Control Autom, Xiamen, China, 2002,2299-2304
[186]Hinrichsen D, Pritchard A J. Stochastic H∞[J]. SIAM J Control Optim,1998,36:1504-1538
[187]Chen B S, Zhang W H. Stochastic H2/H∞ control with state-dependent noise[J]. IEEE Trans Autom Control,2004,49:45-57
[188]Chen B S, Chen W H, Wu H L. Robust Robust H2/H∞ Global Linearization Filter Design for Nonlinear Stochastic Systems[J]. IEEE Trans Circuits Syst I, Reg Papers,2009, 56:1441-1454
[189]Tseng C S. Robust fuzzy filter design for a class of nonlinear stochastic systems[J]. IEEE Trans Fuzzy Syst,2007,15:261-274
[190]Calzolari A, Florchinger P, Nappo G. Nonlinear filtering for stochastic systems with fixed delay:Approximation by a modified Milstein scheme [J]. Comput Math Appl,2011,61: 2498-2509
[191]Wei G, Shu H. H∞ filtering on nonlinear stochastic systems with delay[J]. Chaos Soliton Fract,2007,33:663-670
[192]Qiu J Q, Zhao Y C, Guo S C, et al. Delay-dependent L2-L∞ filter sesign for nonlinear stochastic uncertain time-delay systems[A]. In:Proc ICMLC[C], Qingdao, China,2010, 2:895-900
[193]Zhang W H, Feng G, Li Q H. Robust H∞ Filtering for General Nonlinear Stochastic State-Delayed Systems[J]. Math Probl Eng, doi:10.1155/2012/231352
[194]Shen B, Wang Z D, Hung Y S. Distributed H∞ Filtering for Polynomial Nonlinear S-tochastic Systems in Sensor Networks [J]. IEEE Trans Ind Electron,2011,58:1971-1979
[195]Dong H L, Wang Z D, Gao H J. Robust H∞ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts[J]. IEEE Trans Signal Process,2010,58:1957-1966
[196]Li H P, Shi Y. Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays[J]. Automatica,2012,48:159-166
[197]Wang Z D. and Huang B. Robust H2/H∞ filtering for linear systems with error variance constraints[J]. IEEE Trans Signal Process,2000:2463-2467
[198]Gao H J, Lam J, Xie L H, et al. New approach to mixed H2/H∞ filtering for polytopic discrete-time systems[J]. IEEE Trans Signal Process,2005,53:3183-3192
[199]Qiu J Q, Feng G, Yang J. Improved delay-dependent H∞ filtering design for discrete-time polytopic linear delay systems[J]. IEEE Trans Circuits Syst Ⅱ, Exp Briefs,2008,55: 178-182
[200]Velni J M, Grigoriadis K M. Rate-dependent mixed H2/H∞ filter design for parameter-dependent state delayed LPV systems[J]. IEEE Trans Circuits Syst Ⅰ, Reg Papers,2008, 55:2097-3105
[201]Chen M, Feng G. Delay-dependent H∞ filtering of piecewise linear systems with time-varying delays[J]. IEEE Trans Circuits Syst I, Reg Papers,2008,55:2087-2096
[202]F.W. Yang, Z.D. Wang, D. W. C. Ho, et. al., Robust H2 filtering for a class of systems with stochastic nonlinearities[J]. IEEE Trans. Circuits Syst. Ⅱ, Exp. Briefs,53(3):235-239,2006.
[203]Mendel J. Lessons in Estimation Theory for Signal Processing, Communications and Control[M]. London, U.K.:Prentice-Hall,1995.384-396
[204]Kai X; Wei C L, Liu L D. Robust Extended Kalman Filtering for Nonlinear Systems With Stochastic Uncertainties[J]. IEEE Trans Syst Man Cyber Part A:Systems and Humans, 2010,40:399-405
[205]Li W, Leung H, Zhou Y F. Space-time registration of radar and ESM using unscented Kalman filter[J]. IEEE Trans Aerosp Electron Syst,2004,40:824-836
[206]Kotecha J H, Djuric P M. Gaussian particle filtering[J]. IEEE Trans Signal Process, 2003,51:2592-2601
[207]Wonham W M. Random differential equations in control theory, in Probabilistic Methods in Applied Mathematics[M]. A T B Reid, Ed. New York:Academic,1970,2:131-212
[208]Berman N, Shaked U. H∞ for nonlinear stochastic systems[C]. In:Proc 42nd IEEE Conf Decision Control, Msui, Hawaii USA,2003,5:5025-5030
[209]Oksendal B. Stochastic Differential Equations:An Introduction with Applications[M]. 5th ed. New York:Springer-Verlag,1998.
[210]K. Zhou and P. P. Khargonekar, Robust stabilization of linear systems with norm-bounded time-varying uncertainty [J]. Syst. Control Lett.,1998,10(1):17-20