几类随机时滞非线性系统稳定性分析与综合问题研究
|
摘要
在实际工业控制中存在大量的不确定性(即随机)现象.对于这样的系统,其动态特征都一般难以用精确的数学模型来描述,通常表现出随机特性,而非线性问题也是自然界、工程技术和社会经济等领域经常面临的重要问题,所以随机与非线性的综合问题是具有实际的研究价值,也是研究控制系统的困难所在.正是由于这一原因,控制理论的许多基础且具有代表性的问题长期以来悬而未决.因此,对随机非线性系统的控制问题的研究具有相当大的挑战性,并且具有更加实际的应用价值,值得我们不懈地深入研究.基于以上考虑,本文针对实际系统中可能存在的非线性干扰、外部随机干扰、Markov切换、时间延迟以及参数不确定等因素进行讨论,以线性矩阵不等式(LMI)为工具,以随机控制理论为基础,从而获得系统鲁棒渐近随机稳定或鲁棒指数随机稳定的充分条件.在随机时滞非线性系统的动态特性分析及控制方面,提出了新的思路和给出了新的结果.其主要工作如下：
1.分析研究了一类具有马尔科夫跳变和混合时滞的新型脉冲随机Cohen-Grossberg神经网络的稳定性问题.基于Lyapunov泛函理论和随机控制理论,给出了一组均方意义下的渐近稳定判据,与现有研究结果相比,本文不仅考虑了离散时变时滞,而且也考虑分布时变时滞,所得稳定性判据可以通过求解线性矩阵不等式得到,结果更易验证.另外把所获得的结果扩展到范数有界不确定性的随机时滞脉冲Cohen-Grossberg神经网络系统中.
2.分析研究了一类具有时变时滞和马尔科夫跳变的不确定中立型随机神经网络的鲁棒稳定性问题.首先,建立了一个新型具有随机扰动和马尔科夫跳变的不确定中立型时滞神经网络模型,并且该不确定性是时变和范数有界的.然后,基于Lipschitz连续条件和Schur补技术,给出了具有时滞依赖的稳定性判据,与时滞独立的稳定性判据相比,具有较小的保守性.
3.研究了一类新型时滞随机分布参数系统的模糊控制问题.首先,建立了一个新型的具有多维布朗运动和时变时滞的分布参数系统模型,然后,基于Galerkin方法和利用模糊控制理论,给出了具有时滞依赖的闭环系统的渐近稳定性判据.最后,进一步研究系统的保性能控制的问题,通过求解线性矩阵不等式给出了模糊控制器和保性能控制器的设计方法.
4.研究了一类具有时变时滞的随机模糊Hopfield神经网络的全局渐近稳定性问题.基于改进的带有权重依赖拉格朗日乘子的自由权矩阵方法和Jensen积分不等式技术,得到了一种新颖的以线性矩阵不等式形式给出的稳定判据.在推导中应用了参数依赖型的Lyapunov-Krasovskii泛函和一种新的针对三维模糊累加求和的模糊放松技术来减少结果的保守性.在稳定性分析过程中,模糊隶属函数的归一化空间的这一代数性质被充分考虑,从而得到了一系列由线性矩阵不等式组成的放松的稳定性判据.
5.研究了一类具有混合时变时滞和马尔科夫跳变的脉冲中立型神经网络.该系统是采用中立型积分-微分方程的形式所表示,与现有结果相比,具有更广泛的形式.基于Lyapunov-Krasovskii泛函,从而得到了系统时滞依赖的全局指数稳定性判据.另外,把所获得的结果进一步扩展到各不相同的时变时滞的随机脉冲中立型神经网络的模型.
6.研究了一类具有混合时变时滞和乘性噪声的马尔科夫跳变神经网络的时滞依赖随机稳定性问题.通过利用松弛矩阵和马尔科夫跳变的Lyapunov泛函,得到了用线性矩阵不等式描述的新的时滞依赖判据,该判据保证了马尔科夫跳变神经网络的均方意义下的全局渐近稳定性.不同于通常结果,所研究问题的主要特点是混合时变时滞和乘性噪声是依赖于马尔科夫跳变模式的.
最后,指出了基于随机时滞神经网络系统和随机分布参数系统研究中存在的一些问题和发展方向,并对未来的研究工作进行了展望.
The nondeterministic (i.e. stochastic) phenomena are frequently encountered in practice industrial control. These systems'dynamic characteristics are generally difficult to use precise mathematical model to describe, and often show random characteristics. Moreover, the problem of nonlinearities is an important research object faced by the field of nature, engineering technology and the economics. So the difficulties of the investigation for control systems are stochastic and nonlinear, which is more practical in application. It is because of this reason that many basic and typical problems of control theory are unfathomed for a long time. Thus, the investigation for the control theories of stochastic nonlinear systems is a challenge and worthy to investigate, which is more practical in application. As concerned above, in this dissertation, by employing linear matrix inequality (LMI) technique and stochastic control theory, the sufficient conditions are obtained such that the resulting systems are robustly asymptotical or exponential stable in the mean square, for all possible nonlinear disturbances, external stochastic disturbances, Markovian jumping, time delays as well as uncertain parameters. Some novel methods and ideas in the fields of stochastic nonlinear systems with time delay are proposed. The main contents of the dissertation can be briefly described as follows:
1. The problem of dynamics analysis for a class of new impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on LMI forms and stochastic control theory. Com-pared with the existing results, this paper considers not only discrete time-varying delay but also distribute time-varying delay. And the derived criteria can be verified easily checked and solved by LMI Toolbox in Matlab. The proposed methods are extended to the stochastic impulsive Cohen-Grossberg neural networks with either norm-bounded uncertainties or time delay.
2. The robust stability problem of a class of uncertain neutral stochastic neu-ral networks with Markovian jumping and time-varying delays is researched. First, a new model of uncertain neutral stochastic neural networks with stochastic disturbance and Markovian jumping. The parameter uncertain-ties are assumed to be time-varying and norm-bounded. Based on Lipschitz continuity and Schur complement method, the delay-dependent sufficient con-ditions for the above problem are obtained, which is less conservative than the delay-independent ones.
3. The fuzzy control problem of a class of new stochastic distributed parameter system with time delay is researched. First, a new model of distributed param-eter system with multidimensional Brownian motion and time-varying delay. Based on Galerkin's method and fuzzy control theory, the delay-dependent cri-terion of the closed-loop system for the asymptotical stability in mean square are obtained. Finally, the guaranteed cost control problem of the above system is researched, and given the method of fuzzy controller and guaranteed cost controller by using of the solution of linear matrix inequality.
4. The global asymptotical stability problem of stochastic fuzzy Hopfield neural networks with time-varying delays is investigated. Based on the Lyapunov-Krasovskii functional approach, an improved free-weighting matrix approach with weighting-dependent Lagrange multipliers, and the Jensen integral in-equality, novel LMI-based stability criteria are developed by applying a parameter-dependent Lyapunov functional and new fuzzy relaxed techniques for cubic fuzzy summations. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability anal-ysis and the obtained relaxed stability criteria are in terms of Linear matrix inequalities.
5. The stochastic stability problem of neutral-type impulsive neural networks with Markovian jumping and mixed time-varying delays described by a integro-differential equations is concerned. This structure under consideration is more general that those in the other papers. By utilizing the Lyapunov-Krasovkii functional approach, we obtain some novel global exponentially stable results, which are delay-dependent sufficient condition. The proposed methods are extended to the stochastic impulsive neutral neural networks with time-varying delay, which is different from each other.
6. The problem of delay-dependent stochastic stability analysis for nonlinear Markovian jumping neural networks with mixed time-varying delays and multi-plicative noise is considered. By introducing slack matrix variables and Marko- vian jumping Lyapunov functional, some new delay-dependent sufficient con-ditions are obtained in linear matrix inequality (LMI) format which guarantee the system is asymptotically mean-square stable. An important feature of the model is that mixed state delays and multiplicative noise are mode-dependent.
Finally, concluding remarks are given. Some unsolved problems and devel-opment directions for stochastic neural networks with time delay and stochastic distributed parameter system are illustrated. Further, the prospects of the future study are given.
1.分析研究了一类具有马尔科夫跳变和混合时滞的新型脉冲随机Cohen-Grossberg神经网络的稳定性问题.基于Lyapunov泛函理论和随机控制理论,给出了一组均方意义下的渐近稳定判据,与现有研究结果相比,本文不仅考虑了离散时变时滞,而且也考虑分布时变时滞,所得稳定性判据可以通过求解线性矩阵不等式得到,结果更易验证.另外把所获得的结果扩展到范数有界不确定性的随机时滞脉冲Cohen-Grossberg神经网络系统中.
2.分析研究了一类具有时变时滞和马尔科夫跳变的不确定中立型随机神经网络的鲁棒稳定性问题.首先,建立了一个新型具有随机扰动和马尔科夫跳变的不确定中立型时滞神经网络模型,并且该不确定性是时变和范数有界的.然后,基于Lipschitz连续条件和Schur补技术,给出了具有时滞依赖的稳定性判据,与时滞独立的稳定性判据相比,具有较小的保守性.
3.研究了一类新型时滞随机分布参数系统的模糊控制问题.首先,建立了一个新型的具有多维布朗运动和时变时滞的分布参数系统模型,然后,基于Galerkin方法和利用模糊控制理论,给出了具有时滞依赖的闭环系统的渐近稳定性判据.最后,进一步研究系统的保性能控制的问题,通过求解线性矩阵不等式给出了模糊控制器和保性能控制器的设计方法.
4.研究了一类具有时变时滞的随机模糊Hopfield神经网络的全局渐近稳定性问题.基于改进的带有权重依赖拉格朗日乘子的自由权矩阵方法和Jensen积分不等式技术,得到了一种新颖的以线性矩阵不等式形式给出的稳定判据.在推导中应用了参数依赖型的Lyapunov-Krasovskii泛函和一种新的针对三维模糊累加求和的模糊放松技术来减少结果的保守性.在稳定性分析过程中,模糊隶属函数的归一化空间的这一代数性质被充分考虑,从而得到了一系列由线性矩阵不等式组成的放松的稳定性判据.
5.研究了一类具有混合时变时滞和马尔科夫跳变的脉冲中立型神经网络.该系统是采用中立型积分-微分方程的形式所表示,与现有结果相比,具有更广泛的形式.基于Lyapunov-Krasovskii泛函,从而得到了系统时滞依赖的全局指数稳定性判据.另外,把所获得的结果进一步扩展到各不相同的时变时滞的随机脉冲中立型神经网络的模型.
6.研究了一类具有混合时变时滞和乘性噪声的马尔科夫跳变神经网络的时滞依赖随机稳定性问题.通过利用松弛矩阵和马尔科夫跳变的Lyapunov泛函,得到了用线性矩阵不等式描述的新的时滞依赖判据,该判据保证了马尔科夫跳变神经网络的均方意义下的全局渐近稳定性.不同于通常结果,所研究问题的主要特点是混合时变时滞和乘性噪声是依赖于马尔科夫跳变模式的.
最后,指出了基于随机时滞神经网络系统和随机分布参数系统研究中存在的一些问题和发展方向,并对未来的研究工作进行了展望.
The nondeterministic (i.e. stochastic) phenomena are frequently encountered in practice industrial control. These systems'dynamic characteristics are generally difficult to use precise mathematical model to describe, and often show random characteristics. Moreover, the problem of nonlinearities is an important research object faced by the field of nature, engineering technology and the economics. So the difficulties of the investigation for control systems are stochastic and nonlinear, which is more practical in application. It is because of this reason that many basic and typical problems of control theory are unfathomed for a long time. Thus, the investigation for the control theories of stochastic nonlinear systems is a challenge and worthy to investigate, which is more practical in application. As concerned above, in this dissertation, by employing linear matrix inequality (LMI) technique and stochastic control theory, the sufficient conditions are obtained such that the resulting systems are robustly asymptotical or exponential stable in the mean square, for all possible nonlinear disturbances, external stochastic disturbances, Markovian jumping, time delays as well as uncertain parameters. Some novel methods and ideas in the fields of stochastic nonlinear systems with time delay are proposed. The main contents of the dissertation can be briefly described as follows:
1. The problem of dynamics analysis for a class of new impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on LMI forms and stochastic control theory. Com-pared with the existing results, this paper considers not only discrete time-varying delay but also distribute time-varying delay. And the derived criteria can be verified easily checked and solved by LMI Toolbox in Matlab. The proposed methods are extended to the stochastic impulsive Cohen-Grossberg neural networks with either norm-bounded uncertainties or time delay.
2. The robust stability problem of a class of uncertain neutral stochastic neu-ral networks with Markovian jumping and time-varying delays is researched. First, a new model of uncertain neutral stochastic neural networks with stochastic disturbance and Markovian jumping. The parameter uncertain-ties are assumed to be time-varying and norm-bounded. Based on Lipschitz continuity and Schur complement method, the delay-dependent sufficient con-ditions for the above problem are obtained, which is less conservative than the delay-independent ones.
3. The fuzzy control problem of a class of new stochastic distributed parameter system with time delay is researched. First, a new model of distributed param-eter system with multidimensional Brownian motion and time-varying delay. Based on Galerkin's method and fuzzy control theory, the delay-dependent cri-terion of the closed-loop system for the asymptotical stability in mean square are obtained. Finally, the guaranteed cost control problem of the above system is researched, and given the method of fuzzy controller and guaranteed cost controller by using of the solution of linear matrix inequality.
4. The global asymptotical stability problem of stochastic fuzzy Hopfield neural networks with time-varying delays is investigated. Based on the Lyapunov-Krasovskii functional approach, an improved free-weighting matrix approach with weighting-dependent Lagrange multipliers, and the Jensen integral in-equality, novel LMI-based stability criteria are developed by applying a parameter-dependent Lyapunov functional and new fuzzy relaxed techniques for cubic fuzzy summations. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability anal-ysis and the obtained relaxed stability criteria are in terms of Linear matrix inequalities.
5. The stochastic stability problem of neutral-type impulsive neural networks with Markovian jumping and mixed time-varying delays described by a integro-differential equations is concerned. This structure under consideration is more general that those in the other papers. By utilizing the Lyapunov-Krasovkii functional approach, we obtain some novel global exponentially stable results, which are delay-dependent sufficient condition. The proposed methods are extended to the stochastic impulsive neutral neural networks with time-varying delay, which is different from each other.
6. The problem of delay-dependent stochastic stability analysis for nonlinear Markovian jumping neural networks with mixed time-varying delays and multi-plicative noise is considered. By introducing slack matrix variables and Marko- vian jumping Lyapunov functional, some new delay-dependent sufficient con-ditions are obtained in linear matrix inequality (LMI) format which guarantee the system is asymptotically mean-square stable. An important feature of the model is that mixed state delays and multiplicative noise are mode-dependent.
Finally, concluding remarks are given. Some unsolved problems and devel-opment directions for stochastic neural networks with time delay and stochastic distributed parameter system are illustrated. Further, the prospects of the future study are given.
引文
1 Mao X R. Stochastic Differential Equations and Applications[M]. West Sussex, UK:Horwood,1997.
2 Kushner H J. Stochastic stability and control[M]. New York:Academic,1967.
3 Wonham W M. On a matrix Riccati equation of stochastic control[J]. SIAM Journal on Control,1968,6:681-697.
4 Ito K. On stochastic differential equations[J]. Memoirs of the American Math-ematical Society,4:1-51,1951.
5钱学森,宋健.工程控制论[M].北京：科学出版社,1981.
6郭雷.时变随机系统-稳定性、估计与控制[M].长春：吉林科学技术出版社,1993.
7张炳根,赵玉枝.科学与工程中的随机微分方程[M].北京：北京海洋出版社,1980.
8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.
9高钟毓.工程系统中的随机过程-随机系统分析与最优滤波[M].北京：清华大学出版社,1989.
10朱立秋.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.
11钱敏平,龚光鲁.应用随机过程[M].北京：北京大学出版社,1998.
12郭尚来.随机控制[M].北京：清华大学出版社,1999.
13方洋旺.随机系统最优控制[M].北京：清华大学出版社,2006.
14林元烈.应用随机过程[M].北京：清华大学出版社,2007.
15王迎春.不确定随机系统若干控制问题的研究[D].沈阳：东北大学博士论文,2006.
16陈云.杭州：随机时滞系统的分析与综合[D].浙江大学博士论文,2008.
17夏建伟.南京：连续随机时滞系统鲁棒控制和滤波[D].南京理工大学博士论文,2007.
18廖晓昕.稳定性的理论、方法和应用[M].武汉：华中科技大学出版社,2004.
19郑大钟.线性系统理论[M].北京：清华大学出版社,2003.
20 Gao H, Lam J, Wang C, Xu S. Robust H∞ filtering for 2D stochastic systems[J]. Circuits, Systems and Signal Processing,2004,23(6):479-505.
21 Cao Y, Lam J, Hu L. Dleay-dependent stochastic stability and H∞ analysis for time-delay systems with markovian jumping parameters[J]. Journal of Fraklin Institute,2003,340, (6-7):423-434.
22 Shu H, Wei G. H∞ analysis of nonlinear stochastic time-delay systems[J]. Chaos, Solitons and Fractals,2005,26(2):637-647.
23 Yuan C, Mao X. Robust stability and controllability of stochastic differential delay equations with markovian switching[J]. Automatica,2004,40(3):343-354.
24 Wang Z, Yang F, Liu X. Robust filtering for systems with stochastic nonlin-earities and deterministic uncertainties[J]. Pros. IME I:Journal of Systems and Control Engineering,2006,220(3):171-182.
25 Wang Z, Shu H, Liu X. Reliable stabilization of stochastic time-delay systems with nonlinear disturbances [J]. International Journal of General Systems,2005, 34 (5):523-535.
26 Kang Y, Xie Y, Xu J. Observing nonlinear stochastic resonance with piecewise constant driving forces by the method of moments[J]. Chaos, Soditons and Fractals,2006,27(3):715-721.
27 Li W, Xu W, Zhao J, Jin Y. First passage problem for strong nonlinear stochas-tic dynamical systems[J]. Chaos, Solitons and Fractals,2006,28(2):414-421.
28张维海,袁富宇,随机系统的能稳性和精确能控性的关系[J].控制理论与应用,1999,16(3)：419-421.
29 Gao H, Lam J, Wang C. Robust energy-to-peak filter design for stochastic time-delay systems[J]. Systems and Control Letters,2006,55(2):101-111.
30 Gao H, Wang C, Wang J. On H∞ performance analysis for continuous-time stochastic systems with polytopic uncertainties[J]. Circuits, Systems and Signal Processing,2005,24(4):415-429.
31 Xu S, Chen T. Robust H∞ control for uncertain stochastic systems with state delay[J]. IEEE Transactions on Automatic Control,2002,47(12):2089-2094.
32 Liu Y, Wang Z, Liu X. 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.
33 Wang Z, Liu Y, Liu X. H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities[J]. Automatica,2008,44(5):1268-1277.
34 Yue D, Han Q L. Dleay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity and markovian switching[J]. IEEE Trans-actions on Automatic Control,2005,50(2):217-222.
35伏玉笋,田作华,施颂椒.非线性随机系统解耦问题：微分几何方法[J].应用科学学报.2002,20(3)：272-274.
36黄玉林,张维海,李庆华.一类非线性随机不确定系统的鲁棒滤波[J].山东大学学报(理学版).2006,41(2)：278-284.
37 Guo L, Wang H. Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonliner filters[J]. IEEE Transactions on Circuits and Systems-I,2005,52(8):1644-1652.
38 Wang Z, Lam J, Liu X. Exponential filtering for uncertain markovian jump time-delay systems with nonlinear disturbances [J]. IEEE Transactions on Cir-cuits and Systems-Ⅱ,2004,51(5):262-268.
39 Wang Y, Xie L, DeSouza C E. Robust control of a class of uncertain nonlinear systems[J]. Systems and Control Letters,1992,19(2):139-149.
40 Pearson R. Gray-box modeling of nonideal sensors[C]. in Proc. of the 2001 American Control Conf,2001,6:4404-4409.
41 Kreisselmeier G. Stabilization of linear systems in the presence of output mea-surement saturation[J]. Systems and Control letters,1996,29(1):27-30.
42 Lin Z, Hu T. Semi-global stabilization of linear systems subject to output sat-uration[J]. Systems and Control letters,2001,43(3):211-217.
43 Cao Y, Lin Z, Chen B M. An output feedback H∞ controller design for linear systems subject to sensor nonlinearities[J]. IEEE Transactions on Circuits and Systems-I,2003,50:914-921.
44 Han Q L. Absolute stability of time delay systems with sector-bounded nonlin-earity[J]. Automatica,2005,41(12):2171-2176.
45 Yaz E E, Yaz Y I. State estimation of uncertain nonlinear stochastic systems with general criteria[J]. Applsed Mathematics Letters,2001,14(15):605-610.
46 Yang F, Wang Z, Ho D W C, Liu X. Robust H2 filtering for a class of systems with stochastic nonlinearities[J]. IEEE Transactions on Circuits and Systems-II, 2006,53(3):235-239.
47 Wang Z, Yang F, Ho D W C, Liu X. Filtering for stochastic time-delay systems with missing measurements [J]. IEEE Transactions on Signal Processing,2006, 54(7):2579-2587.
48 Wang Z, Liu Y, Li M, Liu X. Stability analysis for stochastic cohen-grossberg neural networks with mixed time delays[J]. IEEE Transactions on Neural Net-works,2006,17(3):814-820.
49 Boukas E K, Liu Z K. Deterministic and stochastic time-delay systems[M]. Boston:Birkhauser,2002.
50 Shi P, Mahmoud M, Nguang S K, Ismail A. Robust filtering for jumping systems with mode-dependent delays[J]. Signal Processing,2006,86(1):140-152.
51 Shi P, Mahmoud M, Yi J, Ismail A. Worst case control of uncertain jumping systems with multi-state and input delay information[J]. Information Sciences, 2005,176(2):186-200.
52 Gao H, Wang C. Robust L2 L2-L∞ filtering for uncertain systems with muti-ple time-varying state delays[J]. IEEE Transactions on Circuits and Systems-I, 2003,50(4):594-599.
53 Abdallah S. Stability and persistence in plankton models with distributed de-lays[J]. Chaos, Solitons and Fractals,2003,17(5):879-884.
54 Chiarella C, Szidarovszky F. Bounded continuously distributed delays in dy-namic oligopolies[J]. Chaos, Solitons and Fractals,2003,18(5):977-993.
55 Hale J. Theory of functional differential equations[M]. New York:Springer-Verlag,1977.
56 Wang Z, Ho D W C. Filtering on nonlinear time-delay stochastic systems[J]. Automatica,2003,39(1):101-109.
57 Wang Z, Goodall D, Burnham K. On designing observers for time-delay systems with nonlinear disturbances [J]. International Journal of Control,2002,75(11): 803-811.
58 Wang Z, Qiao H, Burnham K. On stabilization of bilinear uncertain time-delay stochastic systems with markovian jumping parameters[J]. IEEE Transactions on Automatic Control,2002,47(4):640-646.
59 Wang Z, Huang B, Burnham K. Stochastic reliable control of a class of uncer-tain time-delay systems with unknown nonlinearities[J]. IEEE Transaction on Circuits Systems-I,2001,48(5):646-650.
60 Wang Z, Huang B, Unbehauen H. Robust H∞ observer design of linear state delayed systems with parametric uncertainty:the discrete-time case[J]. Auto-matica,1999,35(6):1161-1167.
61 Chen W, Guan Z, Liu X. Delay-dependent exponential stability of uncertain stochastic systems with mutiple delays:an LMI approach[J]. Systems and Con-trol Letters,2005,54(6):547-555.
62 Gao H, Wang C. Delay-dependent robust H∞ and l2-l∞ filtering for a class of uncertain nonlinear time-delay systems[J]. IEEE Transactions on Automatic Control,2003,48(9):1661-1666.
63 Xu S, Lam J, Mao X, Zou Y. A new LMI condition for delay-dependent robust stability of stochastic time-delay systems[J]. Asian Journal of Control,2005, 7(4):419-423.
64 He Y, Wu M, She J, Liu G. Delay-dependent robust stability criteria for uncer-tain neutral systems with mixed delays[J]. Systems and Control Letters,2004, 51(1):57-65.
65 He Y, Wang Q G, Xie L, Lin C. Further improvement of free-weighting ma-trices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control,2007,52(2):293-299.
66 Xu S, Lam J. Improved delay-dependent stability results for time-delay sys-tems[J]. IEEE Transactions on Automcatic Control,2005,50(3):384-387.
67何勇,吴敏.多时变状态和控制时滞系统的绝对稳定性[J].控制理论与应用,2004,21(4)：595-598.
68 Arnold L. Stochastic Differential Equations:Theory and Applications[M]. John Wiley Sons,1972.
69 Mao X R. Stability of Stochastic Differential Equations with Respect to Semi-martingales [M]. Longman Scientific and Technical,1991.
70 Gaines B R. Stochastic computing system [C]. In:Tou J T, ed. Advances in Information System Science, New York:Plenum,1969:37-172.
71 Poppelbaum W J, Dollas A, Glickman J B, O'Toole C. Unary processing [J]. Advances in Computers,1987,26(1):47-92.
72 Hopfield J J. Learning algorithms and probalility distributions in feed-forward and feed-back networks[C]. Proceeding of the National Academy of Sciences, 1987,84:8429-8433.
73 Hu S, Liao X X, Mao X R. Stochastic Hopfield neural networks[J]. Journal of Physics A:Mathematical and Genreal,2003,36(9):2235-2249.
74 Banerjee A. On the phase-space dynamics of system of spiking neurons I:Model and Experiments [J]. Neural Compatation,2001,13(1):161-193.
75 Banerjee A. On the phase-space dynamics of system of spiking neurons II: formal analysis[J]. Neural Compatation,2001,13(1):195-225.
76 Gerstner W, Kistler W. Spiking Neuron Model:Single Neurons, Populations, Plastixity [M]. UK:Cambridge University Press,2002.
77 Maass W, Bishop C M. Pulse Neural Networks[M]. Cambridge:MIT Press, 1998.
78 Song Q K, Wang Z D. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays [J]. Phys. Lett. A,387(13): 3314-3326.
79 Dong M, Zhang H G, Wang Y C. Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays[J]. Neurocomputing,2009,72(7-9):1999-2004.
80 Alspector J, Gannett J W, Haber S, Parker M S, Chu R. A VLSI-efficient technique for generating multiple uncorrelation noise and its application to stochastic neural networks [J]. IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications,1991,38(1):109-123.
81 Murray A, Tarassenko L. Analogue Neural VLSI-A Pulse Stream Approach[M]. London:Chapman and Hall,1994.
82 Babu G P, Murty M N. Optimal thresholding using multistate stochastic con-nectionist approach[J]. Pattern Recognition Letters,1995,16(1):11-18.
83 Chiou G I, Huang J N. A neural network-based stochastic active contour model (NNS-SNAKE) for contour finding of distinct features[J]. IEEE Transactions Image Process,1995,4(10):1407-1416.
84 Manjunath B S, Simchony T, Chellappa R. Stochastic and deterministic net-works for texture segmentation[J]. IEEE Transactions on Acoustics, Speech and Signal processing,1990,38(6):1039-1049.
85 Grossberg S, Mclonghlin N P. Cortical dynamics of three dimensional surface perception-Binocular and half-occludel scenic images[J]. Neural Networks,1997, 10(9):1583-1605.
86 Raghu P P, Yegnanarayana B. Multispectral image classification using gabor filters and stochastic relaration neural network[J]. Neural Networks,1997,10(3): 561-572.
87 Wang Y M, Wahl F M. Vector-entropy optimization-based neural network ap-proach to image reconstruction from projections[J]. IEEE Transactions on Neu-ral Networks,1997,8(5):1008-1014.
88 Cohen M, Grossberg S. Absolute stability of global pattern formation and par-allel memory storage by competitive neural networks[J]. IEEE Transactions on Systems, Man, and Cybernetics,1983,13(5):815-826.
89 Chua L O, Yang L. Celluar neural networks:Theory[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1988,35(10): 1257-1272.
90 Chua L O, Yang L. Celluar neural networks:Application[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1988,35(10): 1273-1290.
91 Chua L O. CNN:A Paradigm for Complexity[M]. Singapore:World Scientific, 1988.
92 Liu D R. CNN:Cloning template design of cellular neural networks for associa-tive memories[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1997,44(7):646-650.
93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.
94 Wu J H. Theory and Applications of Partial Functional Differential Equa-tions [M]. New York:Springer,1996.
95刘永清,谢胜利.滞后分布参数系统的稳定性与变结构控制[M].广州：华南理工大学出版社,1998.
96张炳根.泛函微分方程振动理论的发展[J].科学通报,1998,43(4)：345-354.
97崔宝同,楼旭阳.时滞分布参数系统理论及其应用[M].北京：国防工业出版社,2009.
98 Benkhalti R, Bouzahir H, Ezzinbi K. Existence of a periodic solution for some partial functional differential equations with infinite delay[J]. J. Math. Anal. Appl.,2001,256:257-280.
99 Hernandez E, Henriquez H R. Existence of periodic solutions of partial neutral functional differential equations with unbounded delay [J]. J. Math. Anal. Appl., 1998,221:499-522.
100 Adimy A, Ezzinbi K, Laklach M. Existence of solutions for a class of partial neutral functional differential equations[J]. Partial Differential Equations,2000, 330:957-962.
101俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京：清华大学出版社,2002.
102 Cao J D, Li H X, Ho D W C. Synchronization criteria of Lur'e systems with time-delay feedback control[J]. Chaos, Solit. & Fract.,2005,23(4):1285-1298.
103 Xie L H, Fu M Y, De souza C E. H∞ control and quadratic stabilization of sys-tems with parameter uncertainty via output feedback[J]. IEEE Trans. Autom. Contr.,1992,37:1253-1256.
104 Wang Y Y, Xie L H, De souza C E. Robust control of a class of uncertain nonlinear systems [J]. Systems & Control Letters,1992,19(2):139-149.
105 Gu K Q. An integral inequality in the stability problem of time-delay sys-tems[C]. Proceedings of 39th IEEE Conference on Decision and Control, Syd-ney, Australia,2000,2805-2810
106 Arik S, Orman Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays[J]. Physics Letters A,2005,341(5-6):410-421.
107 Lu W L, Chen T P. New conditions on global stability of Cohen-Grossberg neural networks[J]. Neural Computation,2003,15(5):1173-1189.
108 Chen T P, Rong L B. Delay-independent stability analysis of Cohen-Grossberg neural networks[J]. Physics Letters A,2003,317(5-6):436-449.
109 Chen T P, Rong L B. Robust global exponential stability of Cohen-Grossberg neural networks with time delays [J]. IEEE Transactions on Neural Networks, 2004,15(1):203-206.
110 Cao J D, Liang J L. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays [J]. Journal of Mathematical Analysis and Applications,2004,296(2):665-685.
111 Cao J D, Li X L. Stability in delayed Cohen-Grossberg neural networks:LMI optimization approach[J]. Physica D,2005,212(1-2):54-65.
112 Song Q K, Cao J D. Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays[J]. Journal of Computa-tional and Applied Mathematics,2006,197(1):188-203。
113 Zhang H G, Ji C. Delay-independent globally asymptotic stability of Cohen-Grossberg neural networks[J]. International Journal of Information And Sys-tems Sciences,2005,1(3-4):221-228.
114 Ji C, Zhang H G, Song C H. LMI approach to robust stability analysis of Cohen-Grossberg neural networks with multiple delays[J]. Lecture Notes in Computer Science,2006,3971:198-203.
115 Yang T. Impulsive control[J]. IEEE Transactions on Automatic Control,1999, 44(5):1081-1083.
116 Yang T. Impulsive System and Control:Theory and Applications[M]. New York:Nova Science Publishers,2001.
117 Li Z G, Wen C Y, Soh Y C. Analysis and design of impulsive control systems[J]. IEEE Transactions on Automatic Control,2001,46(6):894-897.
118 Xu D Y, Yang Z C. Impulsive delay differential inequality and stability of neural networks[J]. J. Math. Anal. Appl,2005,305:107-120.
119 Xu D Y, Zhu W, Long S J. Global exponential stability of impulsive integro-differential equation[J]. Nonlinear Analysis,2006,64(12):2805-2816.
120 Zhang H G, Huang W, Wang Z L. Impulsive control for synchronization of a class chaotic systems[J]. Dynamics of Continuous, Discrete and Impulsive Systems Series B:Applications & Algorithms,2005,12:153-161.
121 Zhang Y, Sun J T. Stability of impulsive neural networks with time delays[J]. Physics Letters A,2005,348(1-2):44-50.
122 Ho D W C, Liang J L, Lam J. Global exponential stability of impulsive high-order BAM neural networks with time-varying delays[J]. Neural Networks,2006, 19(10):1581-1590.
123 Song Q K, Zhang J Y. Global exponential stability of impulsive Cohen-Grossberg neural with time-varying delays[J]. Nonlinear Analysis,2008,9(2): 500-510.
124 Chen Z, Ruan J. Global dynamic analysis of general Cohen-Grossberg neural networks with impulse[J]. Chaos, Solitons and Fractals,2007,32(5):1830-1837.
125 Tino P, Cernansky M, Benuskova L. Markovian architectural bias of recurrent neural networks[J]. IEEE Transactions on Neural Networks,2004,15(1):6-15.
126 Xie L. Stochastic robust stability analysis for Markovian jumping neural net-works with time delays [C], in Proceedings of the IEEE International Conference on Network Sensing Control,2005,923-928.
127 Xie L, Liu T, Lu G D, Wong S T C. Stochastic robust stability analysis for Markovian jump discrete-time delayed neural networks with multiplicative non-linear perturbations [J]. in Lecture Notes in Computer Science,2006,3971:172-178.
128 Wang Z, Liu Y, Yu L, Liu X. Exponential stability of delayed recurrrent neu-ral networks with Markovian jumping parameters[J]. Physics Letters A,2006, 356(4-5):346-352.
129 Huang H, Qu Y Z, Liu H X. Robust stability analysis of switched Hopfield neural networks with time varying delay under uncertainty[J]. Physics Letters A,2005,345(4-6):345-354.
130 Zhao H Y, Ding N. Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays [J]. Applied Mathematics and Computation,2006, 183(1):464-470.
131 Zhang H G, Wang Y C. Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays[J]. IEEE Transac-tions on Neural Networks,2008,19(2):366-370.
132 Yang Z G, Xu D Y, Xiang L. Exponential p-stability of impulsive stochastic differential equations with delays[J]. Physics Letters A,2006,359(2):129-137.
133 Wu H J, Sun J T. P-moment stability of stochastic differential equations with impulsive jump and Markovian switching[J]. Automatica,2006,42(10):1753-1759.
134 Senan S, Arik S. Global robust stability of Bidirectional associative memory neural networks with multiple time delays[J]. IEEE Transactions on Systems, Man, and Cybernetics,2007,37:1375-1381.
135 Mou S S, Gao H J, Lam J, Qiang W Y. A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay[J]. IEEE Transactions on Neural Networks,2008,19(3):532-535.
136 Guo S J, Huang L H. Stability analysis of Cohen-Grossberg neural networks[J]. IEEE Transactions on Neural Networks,2006,17(1):106-117.
137 Zhang H G, Wang Z S, Liu D R. Robust exponential stability of cellular neural networks with multiple time varying delays[J]. IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2007,54(8):730-734.
138 Zhang H G, Wang Z S, Liu D R. Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time varying delays[J]. IEEE Trans-actions on Neural Networks,2008,19(11):1942-1955.
139 Zhang H G, Wang Z S, Liu D R. Global asymptotic stability of recurrent neural networks with multiple time-varying delays [J]. IEEE Transactions on Neural Networks,2008,19(5):855-873.
140 Zhang H G, Wang Z S. Global asymptotic stability of delayed cellular neural networks [J]. IEEE Transactions on Neural Networks,2007,18(3):947-950.
141 Wang Z S, Zhang H G, Yu W. Robust stability of Cohen-Grossberg neural net-works via state transmission matrix[J]. IEEE Transactions on Neural Networks, 2009,20(1):169-174.
142 Zheng C D, Zhang H G, Wang Z S. Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties[J]. Neurocomputing,2009,72(7-9):1744-1754.
143 Wang Z S, Zhang H G. Global asymptotic stability criteria for a class of delayed neural network model of neutral type based on LMI[J]. Control and Decision, 2006,21:527-531.
144 Park J H, Kwon O M, Lee S M. LMI optimization approach on stability for delayed neural networks of neutral-type[J]. Applied Mathematics and Compu-tation,2008,196:236-244.
145 Rakkiyappan R, Balasubramaniam P, Cao J D. Global exponential stability results for neutral-type impulsive neural networks[J]. Nonlinear Analysis:Real World Applications,2010,11:122-130.
146 Park J H, Kwon O M. Global stability for neural networks of neutral-type with interval time-varying delays[J]. Chaos, Solitons & Fractals,2009,41:1174-1181.
147 Feng J, Xu S Y, Zou Y. Delay-dependent stability of neutral type neural net-works with disstributed delays[J]. Neurocomputing,2009,72:2576-2580.
148 Rakkiyappan R, Balasubramaniam P. New global exponential stability results for neutral type neural networks with distributed time delay[J]. Neurocomput-ing,2008,71:1039-1045.
149 Rakkiyappan R, Balasubramaniam P. LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays[J]. Applied Mathematics and Computation,2008,204:317-324.
150 Lou X Y, Cui B T. Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters[J]. Chaos, Solitons & Fractals, 2009,39:2188-2197.
151 Su W W, Chen Y M. Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays[J]. Commun Nonlinear Sci Number Simulat,2009,14:1576-1581.
152 Christofides P D. Control of nonlinear distributed process systems:Recent developments and challenges[J]. AIChE J,2001,47(3):514-518.
153 Curtain R F. Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input[J]. IEEE Transactions on Au-tomatic Control,2005,27(1):98-104.
154 Ray W H. Advanced Process Control[M]. New York:McGraw-Hill,1981.
155 Christofides P D, Daoutidis P. Nonlinear control of diffusion-convection-reaction processes[J]. Computers and Chemical Engineering,1996,20:1071-1076.
156 Christofides P D. Nonlinear and Robust Control of PDE Systems'Methods and Applications to Transport-Reaction Processes[M]. Boston:MA:Birkhauser, 2001.
157 Christofides P D, Daoutidis P. Finite-dimensinal control of parabolic PDE sys-tems using approximate intertial manifolds[J]. J. Math. Anal. Appl,1997,216: 398-420.
158 Takagi T, Sugeno M. Fuzzy identification of system and its applications to modeling and control[J]. IEEE Transactions on Systems, Man and Cybernetics, 1985, SMC-15(1):116-132.
159 Cao Y Y, Frank P M. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach[J]. IEEE Transactions on Fuzzy System,2000,8(2): 200-211.
160 Chen B, Liu X P. Fuzzy guaranteed cost control for nonlinear systems with time-varying delay[J]. IEEE Transactions on Fuzzy System,2005,13(2):238-249.
161 Chen B, Liu X P. Delay-dependent robust H∞ control for T-S fuzzy systems with time delay[J]. IEEE Transactions on Fuzzy System,2005,13(2):544-556.
162 Guan X P, Chen C L. Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays[J]. IEEE Transactions on Fuzzy System,2004,12(2): 236-249.
163 Zhang H G, Cai L L. Decentralized nonlinear control of a HVAC system [J]. IEEE Transactions on Systems, Man and Cybernetics,2002,32(4):493-498.
164 Zhang H G, Quan Y B. Modeling, identification and control of a class of non-linear systems[J]. IEEE Transactions on Fuzzy System,2001,9(2):349-354.
165 Zhang H G, Lun S X, Liu D R. Fuzzy H∞ filter design for a class of nonlinear discrete-time systems with multiple time delay[J]. IEEE Transactions on Fuzzy System,2007,15(3):453-469.
166 Wu H N, Li H X. Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems [J]. IEEE Transactions on Systems, Man and Cybernetics,2007,37(5):1422-1430.
167 Wu H N, Li H X. H∞ fuzzy observer-based control for a class of nonlinear distributed parameter systems with control constraints[J]. IEEE Transactions on Fuzzy System,2008,16(2):502-516.
168 Yuan K, Li H X, Cao J D. Robust stabilization of the ditributed parameter sys-tem with time delay via fuzzy control[J]. IEEE Transactions on Fuzzy System, 2008,16(3):567-584.
169 Hu G S, Lou Y M, Christofides P D. Dynamic output feedback covariance control of stochastic dissipative partial differential equations[J]. Chemical En-gineering Science,2008,63:4531-4542.
170 Boyd S, Ghaoui L E, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory[M]. Philadephia, PA:SIAM,1994.
171 Feng G. A survey on analysis and design of model-based fuzzy control sys-tems[J]. IEEE Transactions on Fuzzy System,2006,14(5):676-697.
172 Li H X, Deng H, Zhong J. Model-based integration of control and supervision for one kind of curing process[J]. IEEE Transactions on Electronics Packaging Manufacturing,2004,27:177-186.
173 E1-Farra N H, Armaou A, Christofides P D. Analysis and control of parabolic PDE systems with input constraints[J]. Automatica,2003,39(4):715-725.
174 Simpson P K. Fuzzy min-max neural networks, part 1:classification[J]. IEEE Trans Neural Networks,1992,3(5):777-786.
175 Buckley J J. Fuzzy neural newtork:a suvrey[J]. Fuzzys and Systems,1994,66: 1-13.
176 Horikawa S, Furuhashi T, Chikawa Y U.On fuzzy modeling using fuzzy neural newtorks with back-propagation algorithm[J]. IEEE Transactions on Neural Networks,1992,3(5):801-806.
177 Lou X Y, Cui B T. Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays[J]. Fuzzy Sets and Systems,2007,158(24): 2746-2756.
178 Ali M S, Balasubramaniam P. Stability analysis of uncertain fuzzy Hopfield neural networks with time delays [J]. Commun Nonlinear Sci Numer Simulat, 2009,14(6):2776-2783.
179 Li H Y, Chen B, Zhou Q, Qian W Y. Robust stability for uncertain delayed fuzzy Hopfield neural networks with markovian jumping parameters[J]. IIEEE Transactions on Systems, Man and Cybernetics, Part B,2009,39(1):94-102.
180 Tanaka K, Hori T, Wang H O. A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions[J]. IEEE Transactions on Fuzzy System,2007,15(3):333-341.
181 Sheng L, Gao M, Yang H Z. Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with timevarying delays[J]. Fuzzy Sets and Systems,2009,160(24):3503-3517.
182 Huang H, Ho D W C, Lam J. Stochastic stability analysis of fuzzy Hopfield neural networks with time-delay[J]. IEEE Transactions on Circuits System II, Briefs,2005,52(4):251-255.
183 Zhang Y M, Shen Y, Liao X X. Robust stability of neutral stochastic interval systems[J]. Journal of Control Theory and Applications,2004,2(1):82-84.
184 She Q Y, Chen L H, Zhang Y M, Guo L. LMI-based stability analysis of neutral Hopfield neural networks[J]. Journal of Southeast University,2005,35:162-164.
185 Xu L G, Xu D Y. Exponential stability of nonlinear impulsive neutral integro-differential equations[J]. Nonlinear Analysis,2008,69:2910-2923.
186 Long S J, Xu D Y. Delay-dependent stability analysis for impulsive neural networks with time varying delays[J]. Neurocomputing,2008,71:1705-1713.
187 Zhang H G, Fu J, Ma T D. Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent interval time-varying delays and multiplicative noise[J]. Chinese Physics B,2009,18(8):3325-3336.
188 Chen W H, Lu X M. Mean square exponential stability of uncertain stochastic delayed neural networks [J]. Physice Letters A,2008,372(7):1061-1069.
189 Li H Y, Chen B, Zhou Q, Fang S L. Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays [J]. Physice Letters A,2008,372(19):3385-3394.
2 Kushner H J. Stochastic stability and control[M]. New York:Academic,1967.
3 Wonham W M. On a matrix Riccati equation of stochastic control[J]. SIAM Journal on Control,1968,6:681-697.
4 Ito K. On stochastic differential equations[J]. Memoirs of the American Math-ematical Society,4:1-51,1951.
5钱学森,宋健.工程控制论[M].北京：科学出版社,1981.
6郭雷.时变随机系统-稳定性、估计与控制[M].长春：吉林科学技术出版社,1993.
7张炳根,赵玉枝.科学与工程中的随机微分方程[M].北京：北京海洋出版社,1980.
8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.
9高钟毓.工程系统中的随机过程-随机系统分析与最优滤波[M].北京：清华大学出版社,1989.
10朱立秋.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.
11钱敏平,龚光鲁.应用随机过程[M].北京：北京大学出版社,1998.
12郭尚来.随机控制[M].北京：清华大学出版社,1999.
13方洋旺.随机系统最优控制[M].北京：清华大学出版社,2006.
14林元烈.应用随机过程[M].北京：清华大学出版社,2007.
15王迎春.不确定随机系统若干控制问题的研究[D].沈阳：东北大学博士论文,2006.
16陈云.杭州：随机时滞系统的分析与综合[D].浙江大学博士论文,2008.
17夏建伟.南京：连续随机时滞系统鲁棒控制和滤波[D].南京理工大学博士论文,2007.
18廖晓昕.稳定性的理论、方法和应用[M].武汉：华中科技大学出版社,2004.
19郑大钟.线性系统理论[M].北京：清华大学出版社,2003.
20 Gao H, Lam J, Wang C, Xu S. Robust H∞ filtering for 2D stochastic systems[J]. Circuits, Systems and Signal Processing,2004,23(6):479-505.
21 Cao Y, Lam J, Hu L. Dleay-dependent stochastic stability and H∞ analysis for time-delay systems with markovian jumping parameters[J]. Journal of Fraklin Institute,2003,340, (6-7):423-434.
22 Shu H, Wei G. H∞ analysis of nonlinear stochastic time-delay systems[J]. Chaos, Solitons and Fractals,2005,26(2):637-647.
23 Yuan C, Mao X. Robust stability and controllability of stochastic differential delay equations with markovian switching[J]. Automatica,2004,40(3):343-354.
24 Wang Z, Yang F, Liu X. Robust filtering for systems with stochastic nonlin-earities and deterministic uncertainties[J]. Pros. IME I:Journal of Systems and Control Engineering,2006,220(3):171-182.
25 Wang Z, Shu H, Liu X. Reliable stabilization of stochastic time-delay systems with nonlinear disturbances [J]. International Journal of General Systems,2005, 34 (5):523-535.
26 Kang Y, Xie Y, Xu J. Observing nonlinear stochastic resonance with piecewise constant driving forces by the method of moments[J]. Chaos, Soditons and Fractals,2006,27(3):715-721.
27 Li W, Xu W, Zhao J, Jin Y. First passage problem for strong nonlinear stochas-tic dynamical systems[J]. Chaos, Solitons and Fractals,2006,28(2):414-421.
28张维海,袁富宇,随机系统的能稳性和精确能控性的关系[J].控制理论与应用,1999,16(3)：419-421.
29 Gao H, Lam J, Wang C. Robust energy-to-peak filter design for stochastic time-delay systems[J]. Systems and Control Letters,2006,55(2):101-111.
30 Gao H, Wang C, Wang J. On H∞ performance analysis for continuous-time stochastic systems with polytopic uncertainties[J]. Circuits, Systems and Signal Processing,2005,24(4):415-429.
31 Xu S, Chen T. Robust H∞ control for uncertain stochastic systems with state delay[J]. IEEE Transactions on Automatic Control,2002,47(12):2089-2094.
32 Liu Y, Wang Z, Liu X. 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.
33 Wang Z, Liu Y, Liu X. H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities[J]. Automatica,2008,44(5):1268-1277.
34 Yue D, Han Q L. Dleay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity and markovian switching[J]. IEEE Trans-actions on Automatic Control,2005,50(2):217-222.
35伏玉笋,田作华,施颂椒.非线性随机系统解耦问题：微分几何方法[J].应用科学学报.2002,20(3)：272-274.
36黄玉林,张维海,李庆华.一类非线性随机不确定系统的鲁棒滤波[J].山东大学学报(理学版).2006,41(2)：278-284.
37 Guo L, Wang H. Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonliner filters[J]. IEEE Transactions on Circuits and Systems-I,2005,52(8):1644-1652.
38 Wang Z, Lam J, Liu X. Exponential filtering for uncertain markovian jump time-delay systems with nonlinear disturbances [J]. IEEE Transactions on Cir-cuits and Systems-Ⅱ,2004,51(5):262-268.
39 Wang Y, Xie L, DeSouza C E. Robust control of a class of uncertain nonlinear systems[J]. Systems and Control Letters,1992,19(2):139-149.
40 Pearson R. Gray-box modeling of nonideal sensors[C]. in Proc. of the 2001 American Control Conf,2001,6:4404-4409.
41 Kreisselmeier G. Stabilization of linear systems in the presence of output mea-surement saturation[J]. Systems and Control letters,1996,29(1):27-30.
42 Lin Z, Hu T. Semi-global stabilization of linear systems subject to output sat-uration[J]. Systems and Control letters,2001,43(3):211-217.
43 Cao Y, Lin Z, Chen B M. An output feedback H∞ controller design for linear systems subject to sensor nonlinearities[J]. IEEE Transactions on Circuits and Systems-I,2003,50:914-921.
44 Han Q L. Absolute stability of time delay systems with sector-bounded nonlin-earity[J]. Automatica,2005,41(12):2171-2176.
45 Yaz E E, Yaz Y I. State estimation of uncertain nonlinear stochastic systems with general criteria[J]. Applsed Mathematics Letters,2001,14(15):605-610.
46 Yang F, Wang Z, Ho D W C, Liu X. Robust H2 filtering for a class of systems with stochastic nonlinearities[J]. IEEE Transactions on Circuits and Systems-II, 2006,53(3):235-239.
47 Wang Z, Yang F, Ho D W C, Liu X. Filtering for stochastic time-delay systems with missing measurements [J]. IEEE Transactions on Signal Processing,2006, 54(7):2579-2587.
48 Wang Z, Liu Y, Li M, Liu X. Stability analysis for stochastic cohen-grossberg neural networks with mixed time delays[J]. IEEE Transactions on Neural Net-works,2006,17(3):814-820.
49 Boukas E K, Liu Z K. Deterministic and stochastic time-delay systems[M]. Boston:Birkhauser,2002.
50 Shi P, Mahmoud M, Nguang S K, Ismail A. Robust filtering for jumping systems with mode-dependent delays[J]. Signal Processing,2006,86(1):140-152.
51 Shi P, Mahmoud M, Yi J, Ismail A. Worst case control of uncertain jumping systems with multi-state and input delay information[J]. Information Sciences, 2005,176(2):186-200.
52 Gao H, Wang C. Robust L2 L2-L∞ filtering for uncertain systems with muti-ple time-varying state delays[J]. IEEE Transactions on Circuits and Systems-I, 2003,50(4):594-599.
53 Abdallah S. Stability and persistence in plankton models with distributed de-lays[J]. Chaos, Solitons and Fractals,2003,17(5):879-884.
54 Chiarella C, Szidarovszky F. Bounded continuously distributed delays in dy-namic oligopolies[J]. Chaos, Solitons and Fractals,2003,18(5):977-993.
55 Hale J. Theory of functional differential equations[M]. New York:Springer-Verlag,1977.
56 Wang Z, Ho D W C. Filtering on nonlinear time-delay stochastic systems[J]. Automatica,2003,39(1):101-109.
57 Wang Z, Goodall D, Burnham K. On designing observers for time-delay systems with nonlinear disturbances [J]. International Journal of Control,2002,75(11): 803-811.
58 Wang Z, Qiao H, Burnham K. On stabilization of bilinear uncertain time-delay stochastic systems with markovian jumping parameters[J]. IEEE Transactions on Automatic Control,2002,47(4):640-646.
59 Wang Z, Huang B, Burnham K. Stochastic reliable control of a class of uncer-tain time-delay systems with unknown nonlinearities[J]. IEEE Transaction on Circuits Systems-I,2001,48(5):646-650.
60 Wang Z, Huang B, Unbehauen H. Robust H∞ observer design of linear state delayed systems with parametric uncertainty:the discrete-time case[J]. Auto-matica,1999,35(6):1161-1167.
61 Chen W, Guan Z, Liu X. Delay-dependent exponential stability of uncertain stochastic systems with mutiple delays:an LMI approach[J]. Systems and Con-trol Letters,2005,54(6):547-555.
62 Gao H, Wang C. Delay-dependent robust H∞ and l2-l∞ filtering for a class of uncertain nonlinear time-delay systems[J]. IEEE Transactions on Automatic Control,2003,48(9):1661-1666.
63 Xu S, Lam J, Mao X, Zou Y. A new LMI condition for delay-dependent robust stability of stochastic time-delay systems[J]. Asian Journal of Control,2005, 7(4):419-423.
64 He Y, Wu M, She J, Liu G. Delay-dependent robust stability criteria for uncer-tain neutral systems with mixed delays[J]. Systems and Control Letters,2004, 51(1):57-65.
65 He Y, Wang Q G, Xie L, Lin C. Further improvement of free-weighting ma-trices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control,2007,52(2):293-299.
66 Xu S, Lam J. Improved delay-dependent stability results for time-delay sys-tems[J]. IEEE Transactions on Automcatic Control,2005,50(3):384-387.
67何勇,吴敏.多时变状态和控制时滞系统的绝对稳定性[J].控制理论与应用,2004,21(4)：595-598.
68 Arnold L. Stochastic Differential Equations:Theory and Applications[M]. John Wiley Sons,1972.
69 Mao X R. Stability of Stochastic Differential Equations with Respect to Semi-martingales [M]. Longman Scientific and Technical,1991.
70 Gaines B R. Stochastic computing system [C]. In:Tou J T, ed. Advances in Information System Science, New York:Plenum,1969:37-172.
71 Poppelbaum W J, Dollas A, Glickman J B, O'Toole C. Unary processing [J]. Advances in Computers,1987,26(1):47-92.
72 Hopfield J J. Learning algorithms and probalility distributions in feed-forward and feed-back networks[C]. Proceeding of the National Academy of Sciences, 1987,84:8429-8433.
73 Hu S, Liao X X, Mao X R. Stochastic Hopfield neural networks[J]. Journal of Physics A:Mathematical and Genreal,2003,36(9):2235-2249.
74 Banerjee A. On the phase-space dynamics of system of spiking neurons I:Model and Experiments [J]. Neural Compatation,2001,13(1):161-193.
75 Banerjee A. On the phase-space dynamics of system of spiking neurons II: formal analysis[J]. Neural Compatation,2001,13(1):195-225.
76 Gerstner W, Kistler W. Spiking Neuron Model:Single Neurons, Populations, Plastixity [M]. UK:Cambridge University Press,2002.
77 Maass W, Bishop C M. Pulse Neural Networks[M]. Cambridge:MIT Press, 1998.
78 Song Q K, Wang Z D. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays [J]. Phys. Lett. A,387(13): 3314-3326.
79 Dong M, Zhang H G, Wang Y C. Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays[J]. Neurocomputing,2009,72(7-9):1999-2004.
80 Alspector J, Gannett J W, Haber S, Parker M S, Chu R. A VLSI-efficient technique for generating multiple uncorrelation noise and its application to stochastic neural networks [J]. IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications,1991,38(1):109-123.
81 Murray A, Tarassenko L. Analogue Neural VLSI-A Pulse Stream Approach[M]. London:Chapman and Hall,1994.
82 Babu G P, Murty M N. Optimal thresholding using multistate stochastic con-nectionist approach[J]. Pattern Recognition Letters,1995,16(1):11-18.
83 Chiou G I, Huang J N. A neural network-based stochastic active contour model (NNS-SNAKE) for contour finding of distinct features[J]. IEEE Transactions Image Process,1995,4(10):1407-1416.
84 Manjunath B S, Simchony T, Chellappa R. Stochastic and deterministic net-works for texture segmentation[J]. IEEE Transactions on Acoustics, Speech and Signal processing,1990,38(6):1039-1049.
85 Grossberg S, Mclonghlin N P. Cortical dynamics of three dimensional surface perception-Binocular and half-occludel scenic images[J]. Neural Networks,1997, 10(9):1583-1605.
86 Raghu P P, Yegnanarayana B. Multispectral image classification using gabor filters and stochastic relaration neural network[J]. Neural Networks,1997,10(3): 561-572.
87 Wang Y M, Wahl F M. Vector-entropy optimization-based neural network ap-proach to image reconstruction from projections[J]. IEEE Transactions on Neu-ral Networks,1997,8(5):1008-1014.
88 Cohen M, Grossberg S. Absolute stability of global pattern formation and par-allel memory storage by competitive neural networks[J]. IEEE Transactions on Systems, Man, and Cybernetics,1983,13(5):815-826.
89 Chua L O, Yang L. Celluar neural networks:Theory[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1988,35(10): 1257-1272.
90 Chua L O, Yang L. Celluar neural networks:Application[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1988,35(10): 1273-1290.
91 Chua L O. CNN:A Paradigm for Complexity[M]. Singapore:World Scientific, 1988.
92 Liu D R. CNN:Cloning template design of cellular neural networks for associa-tive memories[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1997,44(7):646-650.
93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.
94 Wu J H. Theory and Applications of Partial Functional Differential Equa-tions [M]. New York:Springer,1996.
95刘永清,谢胜利.滞后分布参数系统的稳定性与变结构控制[M].广州：华南理工大学出版社,1998.
96张炳根.泛函微分方程振动理论的发展[J].科学通报,1998,43(4)：345-354.
97崔宝同,楼旭阳.时滞分布参数系统理论及其应用[M].北京：国防工业出版社,2009.
98 Benkhalti R, Bouzahir H, Ezzinbi K. Existence of a periodic solution for some partial functional differential equations with infinite delay[J]. J. Math. Anal. Appl.,2001,256:257-280.
99 Hernandez E, Henriquez H R. Existence of periodic solutions of partial neutral functional differential equations with unbounded delay [J]. J. Math. Anal. Appl., 1998,221:499-522.
100 Adimy A, Ezzinbi K, Laklach M. Existence of solutions for a class of partial neutral functional differential equations[J]. Partial Differential Equations,2000, 330:957-962.
101俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京：清华大学出版社,2002.
102 Cao J D, Li H X, Ho D W C. Synchronization criteria of Lur'e systems with time-delay feedback control[J]. Chaos, Solit. & Fract.,2005,23(4):1285-1298.
103 Xie L H, Fu M Y, De souza C E. H∞ control and quadratic stabilization of sys-tems with parameter uncertainty via output feedback[J]. IEEE Trans. Autom. Contr.,1992,37:1253-1256.
104 Wang Y Y, Xie L H, De souza C E. Robust control of a class of uncertain nonlinear systems [J]. Systems & Control Letters,1992,19(2):139-149.
105 Gu K Q. An integral inequality in the stability problem of time-delay sys-tems[C]. Proceedings of 39th IEEE Conference on Decision and Control, Syd-ney, Australia,2000,2805-2810
106 Arik S, Orman Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays[J]. Physics Letters A,2005,341(5-6):410-421.
107 Lu W L, Chen T P. New conditions on global stability of Cohen-Grossberg neural networks[J]. Neural Computation,2003,15(5):1173-1189.
108 Chen T P, Rong L B. Delay-independent stability analysis of Cohen-Grossberg neural networks[J]. Physics Letters A,2003,317(5-6):436-449.
109 Chen T P, Rong L B. Robust global exponential stability of Cohen-Grossberg neural networks with time delays [J]. IEEE Transactions on Neural Networks, 2004,15(1):203-206.
110 Cao J D, Liang J L. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays [J]. Journal of Mathematical Analysis and Applications,2004,296(2):665-685.
111 Cao J D, Li X L. Stability in delayed Cohen-Grossberg neural networks:LMI optimization approach[J]. Physica D,2005,212(1-2):54-65.
112 Song Q K, Cao J D. Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays[J]. Journal of Computa-tional and Applied Mathematics,2006,197(1):188-203。
113 Zhang H G, Ji C. Delay-independent globally asymptotic stability of Cohen-Grossberg neural networks[J]. International Journal of Information And Sys-tems Sciences,2005,1(3-4):221-228.
114 Ji C, Zhang H G, Song C H. LMI approach to robust stability analysis of Cohen-Grossberg neural networks with multiple delays[J]. Lecture Notes in Computer Science,2006,3971:198-203.
115 Yang T. Impulsive control[J]. IEEE Transactions on Automatic Control,1999, 44(5):1081-1083.
116 Yang T. Impulsive System and Control:Theory and Applications[M]. New York:Nova Science Publishers,2001.
117 Li Z G, Wen C Y, Soh Y C. Analysis and design of impulsive control systems[J]. IEEE Transactions on Automatic Control,2001,46(6):894-897.
118 Xu D Y, Yang Z C. Impulsive delay differential inequality and stability of neural networks[J]. J. Math. Anal. Appl,2005,305:107-120.
119 Xu D Y, Zhu W, Long S J. Global exponential stability of impulsive integro-differential equation[J]. Nonlinear Analysis,2006,64(12):2805-2816.
120 Zhang H G, Huang W, Wang Z L. Impulsive control for synchronization of a class chaotic systems[J]. Dynamics of Continuous, Discrete and Impulsive Systems Series B:Applications & Algorithms,2005,12:153-161.
121 Zhang Y, Sun J T. Stability of impulsive neural networks with time delays[J]. Physics Letters A,2005,348(1-2):44-50.
122 Ho D W C, Liang J L, Lam J. Global exponential stability of impulsive high-order BAM neural networks with time-varying delays[J]. Neural Networks,2006, 19(10):1581-1590.
123 Song Q K, Zhang J Y. Global exponential stability of impulsive Cohen-Grossberg neural with time-varying delays[J]. Nonlinear Analysis,2008,9(2): 500-510.
124 Chen Z, Ruan J. Global dynamic analysis of general Cohen-Grossberg neural networks with impulse[J]. Chaos, Solitons and Fractals,2007,32(5):1830-1837.
125 Tino P, Cernansky M, Benuskova L. Markovian architectural bias of recurrent neural networks[J]. IEEE Transactions on Neural Networks,2004,15(1):6-15.
126 Xie L. Stochastic robust stability analysis for Markovian jumping neural net-works with time delays [C], in Proceedings of the IEEE International Conference on Network Sensing Control,2005,923-928.
127 Xie L, Liu T, Lu G D, Wong S T C. Stochastic robust stability analysis for Markovian jump discrete-time delayed neural networks with multiplicative non-linear perturbations [J]. in Lecture Notes in Computer Science,2006,3971:172-178.
128 Wang Z, Liu Y, Yu L, Liu X. Exponential stability of delayed recurrrent neu-ral networks with Markovian jumping parameters[J]. Physics Letters A,2006, 356(4-5):346-352.
129 Huang H, Qu Y Z, Liu H X. Robust stability analysis of switched Hopfield neural networks with time varying delay under uncertainty[J]. Physics Letters A,2005,345(4-6):345-354.
130 Zhao H Y, Ding N. Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays [J]. Applied Mathematics and Computation,2006, 183(1):464-470.
131 Zhang H G, Wang Y C. Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays[J]. IEEE Transac-tions on Neural Networks,2008,19(2):366-370.
132 Yang Z G, Xu D Y, Xiang L. Exponential p-stability of impulsive stochastic differential equations with delays[J]. Physics Letters A,2006,359(2):129-137.
133 Wu H J, Sun J T. P-moment stability of stochastic differential equations with impulsive jump and Markovian switching[J]. Automatica,2006,42(10):1753-1759.
134 Senan S, Arik S. Global robust stability of Bidirectional associative memory neural networks with multiple time delays[J]. IEEE Transactions on Systems, Man, and Cybernetics,2007,37:1375-1381.
135 Mou S S, Gao H J, Lam J, Qiang W Y. A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay[J]. IEEE Transactions on Neural Networks,2008,19(3):532-535.
136 Guo S J, Huang L H. Stability analysis of Cohen-Grossberg neural networks[J]. IEEE Transactions on Neural Networks,2006,17(1):106-117.
137 Zhang H G, Wang Z S, Liu D R. Robust exponential stability of cellular neural networks with multiple time varying delays[J]. IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2007,54(8):730-734.
138 Zhang H G, Wang Z S, Liu D R. Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time varying delays[J]. IEEE Trans-actions on Neural Networks,2008,19(11):1942-1955.
139 Zhang H G, Wang Z S, Liu D R. Global asymptotic stability of recurrent neural networks with multiple time-varying delays [J]. IEEE Transactions on Neural Networks,2008,19(5):855-873.
140 Zhang H G, Wang Z S. Global asymptotic stability of delayed cellular neural networks [J]. IEEE Transactions on Neural Networks,2007,18(3):947-950.
141 Wang Z S, Zhang H G, Yu W. Robust stability of Cohen-Grossberg neural net-works via state transmission matrix[J]. IEEE Transactions on Neural Networks, 2009,20(1):169-174.
142 Zheng C D, Zhang H G, Wang Z S. Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties[J]. Neurocomputing,2009,72(7-9):1744-1754.
143 Wang Z S, Zhang H G. Global asymptotic stability criteria for a class of delayed neural network model of neutral type based on LMI[J]. Control and Decision, 2006,21:527-531.
144 Park J H, Kwon O M, Lee S M. LMI optimization approach on stability for delayed neural networks of neutral-type[J]. Applied Mathematics and Compu-tation,2008,196:236-244.
145 Rakkiyappan R, Balasubramaniam P, Cao J D. Global exponential stability results for neutral-type impulsive neural networks[J]. Nonlinear Analysis:Real World Applications,2010,11:122-130.
146 Park J H, Kwon O M. Global stability for neural networks of neutral-type with interval time-varying delays[J]. Chaos, Solitons & Fractals,2009,41:1174-1181.
147 Feng J, Xu S Y, Zou Y. Delay-dependent stability of neutral type neural net-works with disstributed delays[J]. Neurocomputing,2009,72:2576-2580.
148 Rakkiyappan R, Balasubramaniam P. New global exponential stability results for neutral type neural networks with distributed time delay[J]. Neurocomput-ing,2008,71:1039-1045.
149 Rakkiyappan R, Balasubramaniam P. LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays[J]. Applied Mathematics and Computation,2008,204:317-324.
150 Lou X Y, Cui B T. Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters[J]. Chaos, Solitons & Fractals, 2009,39:2188-2197.
151 Su W W, Chen Y M. Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays[J]. Commun Nonlinear Sci Number Simulat,2009,14:1576-1581.
152 Christofides P D. Control of nonlinear distributed process systems:Recent developments and challenges[J]. AIChE J,2001,47(3):514-518.
153 Curtain R F. Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input[J]. IEEE Transactions on Au-tomatic Control,2005,27(1):98-104.
154 Ray W H. Advanced Process Control[M]. New York:McGraw-Hill,1981.
155 Christofides P D, Daoutidis P. Nonlinear control of diffusion-convection-reaction processes[J]. Computers and Chemical Engineering,1996,20:1071-1076.
156 Christofides P D. Nonlinear and Robust Control of PDE Systems'Methods and Applications to Transport-Reaction Processes[M]. Boston:MA:Birkhauser, 2001.
157 Christofides P D, Daoutidis P. Finite-dimensinal control of parabolic PDE sys-tems using approximate intertial manifolds[J]. J. Math. Anal. Appl,1997,216: 398-420.
158 Takagi T, Sugeno M. Fuzzy identification of system and its applications to modeling and control[J]. IEEE Transactions on Systems, Man and Cybernetics, 1985, SMC-15(1):116-132.
159 Cao Y Y, Frank P M. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach[J]. IEEE Transactions on Fuzzy System,2000,8(2): 200-211.
160 Chen B, Liu X P. Fuzzy guaranteed cost control for nonlinear systems with time-varying delay[J]. IEEE Transactions on Fuzzy System,2005,13(2):238-249.
161 Chen B, Liu X P. Delay-dependent robust H∞ control for T-S fuzzy systems with time delay[J]. IEEE Transactions on Fuzzy System,2005,13(2):544-556.
162 Guan X P, Chen C L. Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays[J]. IEEE Transactions on Fuzzy System,2004,12(2): 236-249.
163 Zhang H G, Cai L L. Decentralized nonlinear control of a HVAC system [J]. IEEE Transactions on Systems, Man and Cybernetics,2002,32(4):493-498.
164 Zhang H G, Quan Y B. Modeling, identification and control of a class of non-linear systems[J]. IEEE Transactions on Fuzzy System,2001,9(2):349-354.
165 Zhang H G, Lun S X, Liu D R. Fuzzy H∞ filter design for a class of nonlinear discrete-time systems with multiple time delay[J]. IEEE Transactions on Fuzzy System,2007,15(3):453-469.
166 Wu H N, Li H X. Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems [J]. IEEE Transactions on Systems, Man and Cybernetics,2007,37(5):1422-1430.
167 Wu H N, Li H X. H∞ fuzzy observer-based control for a class of nonlinear distributed parameter systems with control constraints[J]. IEEE Transactions on Fuzzy System,2008,16(2):502-516.
168 Yuan K, Li H X, Cao J D. Robust stabilization of the ditributed parameter sys-tem with time delay via fuzzy control[J]. IEEE Transactions on Fuzzy System, 2008,16(3):567-584.
169 Hu G S, Lou Y M, Christofides P D. Dynamic output feedback covariance control of stochastic dissipative partial differential equations[J]. Chemical En-gineering Science,2008,63:4531-4542.
170 Boyd S, Ghaoui L E, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory[M]. Philadephia, PA:SIAM,1994.
171 Feng G. A survey on analysis and design of model-based fuzzy control sys-tems[J]. IEEE Transactions on Fuzzy System,2006,14(5):676-697.
172 Li H X, Deng H, Zhong J. Model-based integration of control and supervision for one kind of curing process[J]. IEEE Transactions on Electronics Packaging Manufacturing,2004,27:177-186.
173 E1-Farra N H, Armaou A, Christofides P D. Analysis and control of parabolic PDE systems with input constraints[J]. Automatica,2003,39(4):715-725.
174 Simpson P K. Fuzzy min-max neural networks, part 1:classification[J]. IEEE Trans Neural Networks,1992,3(5):777-786.
175 Buckley J J. Fuzzy neural newtork:a suvrey[J]. Fuzzys and Systems,1994,66: 1-13.
176 Horikawa S, Furuhashi T, Chikawa Y U.On fuzzy modeling using fuzzy neural newtorks with back-propagation algorithm[J]. IEEE Transactions on Neural Networks,1992,3(5):801-806.
177 Lou X Y, Cui B T. Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays[J]. Fuzzy Sets and Systems,2007,158(24): 2746-2756.
178 Ali M S, Balasubramaniam P. Stability analysis of uncertain fuzzy Hopfield neural networks with time delays [J]. Commun Nonlinear Sci Numer Simulat, 2009,14(6):2776-2783.
179 Li H Y, Chen B, Zhou Q, Qian W Y. Robust stability for uncertain delayed fuzzy Hopfield neural networks with markovian jumping parameters[J]. IIEEE Transactions on Systems, Man and Cybernetics, Part B,2009,39(1):94-102.
180 Tanaka K, Hori T, Wang H O. A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions[J]. IEEE Transactions on Fuzzy System,2007,15(3):333-341.
181 Sheng L, Gao M, Yang H Z. Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with timevarying delays[J]. Fuzzy Sets and Systems,2009,160(24):3503-3517.
182 Huang H, Ho D W C, Lam J. Stochastic stability analysis of fuzzy Hopfield neural networks with time-delay[J]. IEEE Transactions on Circuits System II, Briefs,2005,52(4):251-255.
183 Zhang Y M, Shen Y, Liao X X. Robust stability of neutral stochastic interval systems[J]. Journal of Control Theory and Applications,2004,2(1):82-84.
184 She Q Y, Chen L H, Zhang Y M, Guo L. LMI-based stability analysis of neutral Hopfield neural networks[J]. Journal of Southeast University,2005,35:162-164.
185 Xu L G, Xu D Y. Exponential stability of nonlinear impulsive neutral integro-differential equations[J]. Nonlinear Analysis,2008,69:2910-2923.
186 Long S J, Xu D Y. Delay-dependent stability analysis for impulsive neural networks with time varying delays[J]. Neurocomputing,2008,71:1705-1713.
187 Zhang H G, Fu J, Ma T D. Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent interval time-varying delays and multiplicative noise[J]. Chinese Physics B,2009,18(8):3325-3336.
188 Chen W H, Lu X M. Mean square exponential stability of uncertain stochastic delayed neural networks [J]. Physice Letters A,2008,372(7):1061-1069.
189 Li H Y, Chen B, Zhou Q, Fang S L. Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays [J]. Physice Letters A,2008,372(19):3385-3394.