On Input-to-State Stability of Stochastic Retarded Systems With Markovian Switching

This note develops a Razumikhin-type theorem on pth moment input-to-state stability of hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), which is an improvement of an existing result. An application to hybrid stochastic delay systems verifies the effectiveness of the improved result.

[1]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[2]  Bugong Xu.  Stability of Retarded Dynamical Systems: A Lyapunov Function Approach , 2001 .

[3]  X. Mao.  LaSalle-Type Theorems for Stochastic Differential Delay Equations , 1999 .

[4]  Feiqi Deng,et al.  Stability of Hybrid Stochastic Retarded Systems , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  P. Pepe,et al.  A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems , 2006, Syst. Control. Lett..

[6]  Dong Yue,et al.  Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching , 2005, IEEE Transactions on Automatic Control.

[7]  Shuzhi Sam Ge,et al.  Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays , 2008, Int. J. Control.

[8]  Xinzhi Liu,et al.  Stability theory of hybrid dynamical systems with time delay , 2006, IEEE Trans. Autom. Control..

[9]  Eduardo Sontag,et al.  New characterizations of input-to-state stability , 1996, IEEE Trans. Autom. Control..

[10]  Shengyuan Xu,et al.  Robust H∞ control for uncertain stochastic systems with state delay , 2002, IEEE Trans. Autom. Control..

[11]  El-Kébir Boukas,et al.  Delay-dependent robust stability and H/sub /spl infin// control of jump linear systems with time-delay , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[12]  D. Elworthy.  ASYMPTOTIC METHODS IN THE THEORY OF STOCHASTIC DIFFERENTIAL EQUATIONS , 1992 .

[13]  X. Mao.  Stochastic Functional Differential Equations with Markovian Switching , 2004 .

[14]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[15]  Xuerong Mao,et al.  The improved LaSalle-type theorems for stochastic functional differential equations , 2006 .

[16]  X. Mao,et al.  Stochastic differential delay equations with Markovian switching , 2000 .

[17]  Z. Liu,et al.  Delay-dependent robust stability and H8 control of jump linear systems , 2001 .

[18]  Zhe Yang,et al.  Comparison theorem of one-dimensional stochastic hybrid delay systems , 2008, Syst. Control. Lett..

[19]  A. Teel.  Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem , 1998, IEEE Trans. Autom. Control..

[20]  X. Mao.  Razumikhin-type theorems on exponential stability of stochastic functional differential equations , 1996 .

[21]  Michael Athans,et al.  Command and control (C2) theory: A challenge to control science , 1986 .

[22]  Shengyuan Xu,et al.  Razumikhin method and exponential stability of hybrid stochastic delay interval systems , 2006 .

[23]  Feiqi Deng,et al.  Razumikhin-Type Theorems on Stability of Neutral Stochastic Functional Differential Equations , 2008, IEEE Transactions on Automatic Control.

[24]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[25]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[26]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[27]  Fernando Paganini,et al.  A Course in Robust Control Theory , 2000 .

[28]  M. K. Ghosh,et al.  Optimal control of switching diffusions with application to flexible manufacturing systems , 1993 .

[29]  Yi Shen,et al.  New criteria on exponential stability of neutral stochastic differential delay equations , 2006, Syst. Control. Lett..

[30]  X. Mao.  A note on the LaSalle-type theorems for stochastic differential delay equations , 2002 .

[31]  R. Rogers,et al.  An LQ-solution to a control problem associated with a solar thermal central receiver , 1983 .

[32]  Yun Zou,et al.  Robust exponential stabilization for Markovian jump systems with mode-dependent input delay , 2007, Autom..

[33]  Zhong-Ping Jiang,et al.  Global Output-Feedback Stabilization for a Class of Stochastic Non-Minimum-Phase Nonlinear Systems , 2007, 2007 IEEE International Conference on Control Applications.

[34]  Hassan K. Khalil,et al.  Nonlinear Systems Third Edition , 2008 .

[35]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[36]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[37]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

[38]  Gopal K. Basak,et al.  Stability of a Random diffusion with linear drift , 1996 .

[39]  Xuerong Mao,et al.  Stability in distribution of stochastic differential delay equations with Markovian switching , 2003, Syst. Control. Lett..