Boundary Stabilization of Stochastic Delay Reaction-Diffusion Systems
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- 英文论文题名：Boundary Stabilization of Stochastic Delay Reaction-Diffusion Systems
- 论文作者：Xiao-Zhen Liu ; Xiao-Hua Ding ; Kai-Ning Wu
- 英文论文作者：Xiao-Zhen Liu ; Xiao-Hua Ding ; Kai-Ning Wu ; Department of Mathematics ; Harbin Institute of Technology at Weihai
- 年：2017
- 作者机构：Department of Mathematics,Harbin Institute of Technology at Weihai;
- 英文论文关键词：Stochastic Reaction-Diffusion Systems ; Delay ; Boundary Control ; Stabilization ; H Infinity Performance
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O175;O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：350k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers the boundary stabilization of stochastic delay reaction-diffusion systems(SDRDSs).We present the integral-form Lyapunov stability lemma for SDRDSs which provides the foundation of stability analysis for stochastic reaction-diffusion systems. Then, we design a boundary controller and obtain a criterion to guarantee the globally stochastically asymptotical stability of SDRDSs with Neumann boundary conditions. In addition, when the external disturbances enter in a given systems, we design a boundary controller and get the sufficient condition for the mean-square H∞ performance. Two numerical examples verifying the validity of the results are obtained in this paper.
This paper considers the boundary stabilization of stochastic delay reaction-diffusion systems(SDRDSs).We present the integral-form Lyapunov stability lemma for SDRDSs which provides the foundation of stability analysis for stochastic reaction-diffusion systems. Then, we design a boundary controller and obtain a criterion to guarantee the globally stochastically asymptotical stability of SDRDSs with Neumann boundary conditions. In addition, when the external disturbances enter in a given systems, we design a boundary controller and get the sufficient condition for the mean-square H∞ performance. Two numerical examples verifying the validity of the results are obtained in this paper.
This paper considers the boundary stabilization of stochastic delay reaction-diffusion systems(SDRDSs).We present the integral-form Lyapunov stability lemma for SDRDSs which provides the foundation of stability analysis for stochastic reaction-diffusion systems. Then, we design a boundary controller and obtain a criterion to guarantee the globally stochastically asymptotical stability of SDRDSs with Neumann boundary conditions. In addition, when the external disturbances enter in a given systems, we design a boundary controller and get the sufficient condition for the mean-square H∞ performance. Two numerical examples verifying the validity of the results are obtained in this paper.
引文
[1]C.Zhang,W.Li,K.Wang,Graph theory-based approach for stability analysis of stochastic coupled systems with Lévy noise on networks,IEEE Transactions on Neural Networks and Learning Systems,26(8):1698–1709,2005.
[2]H.Zhang,Z.Wu,Y.Xia,Exponential stability of stochastic systems with hysteresis switching,Automatica,50(2):599–606,2014.
[3]J.Yin,S.Khoo,Z.Man,X.Yu,Finite-time stability and instability of stochastic nonlinear systems,Automatica,47(12):2671–2677,2011.
[4]Y.Yang,J.Li,G.Chen,Finite-time stability and stabilization of nonlinear stochastic hybrid systems,Journal of Mathematical Analysis and Applications,356(1):338–345,2009.
[5]Y.Cao,Z.Zeng,T.Huang,New criteria of robust H∞stability for fuzzy mixed-delay systems with nonlinear noise disturbances,Circuits,Systems,and Signal Processing,35(8):2810–2831,2016.
[6]C.Jeong,P.Park,S.Kim,Improved approach to robust stability and H∞performance analysis for systems with an interval time-varying delay,Applied Mathematics and Computation,218(21):10533–10541,2012.
[7]J.Pan,X.Liu,S.Zhong,Stability criteria for impulsive reaction-diffusion Cohen-Grrossberg neural networks with time-varying delays,Mathematical and Couputer Modelling,51(9):1037–1050,2010.
[8]Y.Li,K.Zhao,Robust stability of delayed reaction-diffusion recurrent neural networks wih Dirichlet boundary conditions on time scales,Neurocomputing,74(10):1631–1637,2011.
[9]Y.Kao,C.Wang,H.Karimi,Global stability of coupled Markovian switching reaction-diffusion systems on networks,Nonlinear Analysis-Hybrid Systems,13:61–73,2014.
[10]Q.Luo,Y.Zhang,Asymptotic stability in probability of stochastic reaction diffusion systems,Dynamics of Continuous,Discrete and Impulsive Systems Series B:Applications and Algorithms,16(1):139–149,2009.
[11]Q.Luo,Y.Zhang,Almost sure exponential stability of stochastic reaction diffusion systems,Nonlinear Analysis,71(12):e487–e493,2009.
[12]P.Balasubramaniam,C.Vidhya,Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters,Expert Systems with Applications,39(3):3109–3115,2012.
[13]S.Wirkus,R.Rand,The dynamics of two coupled van der Pol oscillators with delay coupling,Nonlinear dynamics,30(3):205–221,2002.
[14]R.Datko,J.Lagnese,M.Polis,An example on the effect of time delays in boundary feedback stabilization of wave equations,SIAM Journal on Control and Optimization,24(1):152–156,1986.
[15]S.Xu,J.Lam,Improved delay-dependent stability criteria for time-delay systems,IEEE Transactions on Automatic Control,50(3):384–387,2005.
[16]H.Shao,New delay-dependent stability criteria for systems with interval delay,Automatica,45(3):744–749,2009.
[17]Q.Gao,X.Liu,Stabilizing a class of dynamical complex networks based on decentralized control,Control conference,383(2):424–428,2007.
[18]W.Lu,X.Li,Z.Rong,Global stabilization of complex networks with digraph topologies via a local pinning algorithm,Automatica,46(1):116–121,2010.
[19]C.Wen,J.Zhou,Z.Liu,Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,IEEE Transactions on Automatic Control,56(7):1672–1678,2011.
[20]Y.Wang,M.Yang,H.Wang,Robust stabilization of complex switched networks with parametric uncertainties and delays via impulsive control,IEEE International Solid-state Circuits Conference,47(1):136-138,2011.
[21]P.Pan,J.Wang,K.Wu,Boundary stabilization and H∞control for stochastic reaction-diffusion systems,2016 Chinese Control and Decision Conference,2279–2283,2016.
[22]G.Hagen,Absolute stability via boundary control of a semilinear parabolic PDE,IEEE Transactions on Automatic Control,51(3):489–493,2006.
[23]J.Villegas,H.Zwart,Y.Le Gorrec,Exponential stability of a class of boundary control systems,IEEE Transactions on Automatic Control,54(1):142–147,2009.
[24]Y.Kao,C.Wang,Global stability analysis for stochastic coupled reaction-diffusion systems on networks,Nonlinear Analysis:Real World Applications,14(3):1457–1465,2013.
[25]H.Wu,J.Wang,H.Li,Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems,IEEE Transactions on Fuzzy Systems,22(3):642–652,2014.
[26]X.Mao,Stochastic differential equations and their applications,Horwood Publishing,Chichester,1997.
[2]H.Zhang,Z.Wu,Y.Xia,Exponential stability of stochastic systems with hysteresis switching,Automatica,50(2):599–606,2014.
[3]J.Yin,S.Khoo,Z.Man,X.Yu,Finite-time stability and instability of stochastic nonlinear systems,Automatica,47(12):2671–2677,2011.
[4]Y.Yang,J.Li,G.Chen,Finite-time stability and stabilization of nonlinear stochastic hybrid systems,Journal of Mathematical Analysis and Applications,356(1):338–345,2009.
[5]Y.Cao,Z.Zeng,T.Huang,New criteria of robust H∞stability for fuzzy mixed-delay systems with nonlinear noise disturbances,Circuits,Systems,and Signal Processing,35(8):2810–2831,2016.
[6]C.Jeong,P.Park,S.Kim,Improved approach to robust stability and H∞performance analysis for systems with an interval time-varying delay,Applied Mathematics and Computation,218(21):10533–10541,2012.
[7]J.Pan,X.Liu,S.Zhong,Stability criteria for impulsive reaction-diffusion Cohen-Grrossberg neural networks with time-varying delays,Mathematical and Couputer Modelling,51(9):1037–1050,2010.
[8]Y.Li,K.Zhao,Robust stability of delayed reaction-diffusion recurrent neural networks wih Dirichlet boundary conditions on time scales,Neurocomputing,74(10):1631–1637,2011.
[9]Y.Kao,C.Wang,H.Karimi,Global stability of coupled Markovian switching reaction-diffusion systems on networks,Nonlinear Analysis-Hybrid Systems,13:61–73,2014.
[10]Q.Luo,Y.Zhang,Asymptotic stability in probability of stochastic reaction diffusion systems,Dynamics of Continuous,Discrete and Impulsive Systems Series B:Applications and Algorithms,16(1):139–149,2009.
[11]Q.Luo,Y.Zhang,Almost sure exponential stability of stochastic reaction diffusion systems,Nonlinear Analysis,71(12):e487–e493,2009.
[12]P.Balasubramaniam,C.Vidhya,Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters,Expert Systems with Applications,39(3):3109–3115,2012.
[13]S.Wirkus,R.Rand,The dynamics of two coupled van der Pol oscillators with delay coupling,Nonlinear dynamics,30(3):205–221,2002.
[14]R.Datko,J.Lagnese,M.Polis,An example on the effect of time delays in boundary feedback stabilization of wave equations,SIAM Journal on Control and Optimization,24(1):152–156,1986.
[15]S.Xu,J.Lam,Improved delay-dependent stability criteria for time-delay systems,IEEE Transactions on Automatic Control,50(3):384–387,2005.
[16]H.Shao,New delay-dependent stability criteria for systems with interval delay,Automatica,45(3):744–749,2009.
[17]Q.Gao,X.Liu,Stabilizing a class of dynamical complex networks based on decentralized control,Control conference,383(2):424–428,2007.
[18]W.Lu,X.Li,Z.Rong,Global stabilization of complex networks with digraph topologies via a local pinning algorithm,Automatica,46(1):116–121,2010.
[19]C.Wen,J.Zhou,Z.Liu,Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,IEEE Transactions on Automatic Control,56(7):1672–1678,2011.
[20]Y.Wang,M.Yang,H.Wang,Robust stabilization of complex switched networks with parametric uncertainties and delays via impulsive control,IEEE International Solid-state Circuits Conference,47(1):136-138,2011.
[21]P.Pan,J.Wang,K.Wu,Boundary stabilization and H∞control for stochastic reaction-diffusion systems,2016 Chinese Control and Decision Conference,2279–2283,2016.
[22]G.Hagen,Absolute stability via boundary control of a semilinear parabolic PDE,IEEE Transactions on Automatic Control,51(3):489–493,2006.
[23]J.Villegas,H.Zwart,Y.Le Gorrec,Exponential stability of a class of boundary control systems,IEEE Transactions on Automatic Control,54(1):142–147,2009.
[24]Y.Kao,C.Wang,Global stability analysis for stochastic coupled reaction-diffusion systems on networks,Nonlinear Analysis:Real World Applications,14(3):1457–1465,2013.
[25]H.Wu,J.Wang,H.Li,Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems,IEEE Transactions on Fuzzy Systems,22(3):642–652,2014.
[26]X.Mao,Stochastic differential equations and their applications,Horwood Publishing,Chichester,1997.
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