Observer-based controller design for singular stochastic Markov jump systems with state dependent noise

This paper is concerned with the problem of observer-based controller design for singular stochastic Markov jump systems with state-dependent noise. Two concepts called “non-impulsiveness” and “mean square admissibility” are introduced, which are different from previous ones. Sufficient conditions for the open- and closed-loop singular stochastic Markov jump systems with state-dependent noise to be mean square admissible are provided in terms of strict LMIs. The controller gain and the observer gain which guarantee the resulting closed-loop error system to be mean square admissible are obtained in turn by solving the strict LMIs. A numerical example is presented to show the efficiency of the design approach.

[1]  E. Boukas,et al.  Observer-based controller design for linear singular systems with Markovian switching , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[2]  Chenghui Zhang,et al.  H∞ control for discrete-time singular Markov jump systems subject to actuator saturation , 2012, J. Frankl. Inst..

[3]  Peng Shi,et al.  Observer-based finite-time H∞ control for discrete singular stochastic systems , 2014, Appl. Math. Lett..

[4]  El-Kébir Boukas,et al.  On stability and stabilisation of continuoustime singular markovian switching systems , 2008 .

[5]  S. Aachen.  Stochastic Differential Equations An Introduction With Applications , 2016 .

[6]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[7]  S. Campbell.  Singular Systems of Differential Equations , 1980 .

[8]  Bor-Sen Chen,et al.  Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion , 2008, IEEE Transactions on Automatic Control.

[9]  Chenghui Zhang,et al.  Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems , 2008 .

[10]  Bor-Sen Chen,et al.  On stabilizability and exact observability of stochastic systems with their applications , 2023, Autom..

[11]  Shengyuan Xu,et al.  Robust control of descriptor discrete-time Markovian jump systems , 2007, Int. J. Control.

[12]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[13]  Mohamed Darouach,et al.  Observers for Singular Fractional-Order Systems , 2011 .

[14]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[15]  Shengyuan Xu,et al.  On Stability and Stabilizability of Singular Stochastic Systems with Delays , 2005 .

[16]  Zhiwei Gao,et al.  Observer-based controller design for stochastic descriptor systems with Brownian motions , 2013, Autom..

[17]  Tao Liu,et al.  Analytical design of a generalised predictor-based control scheme for low-order integrating and unstable systems with long time delay , 2016 .

[18]  Yuanqing Xia,et al.  Control for discrete singular hybrid systems , 2008, Autom..

[19]  F. Lewis.  A survey of linear singular systems , 1986 .

[20]  L. Dai.  Observers for discrete singular systems , 1988 .

[21]  E. Boukas.  Stabilization of stochastic singular nonlinear hybrid systems , 2006 .

[22]  Xuerong Mao,et al.  Stability of Singular Stochastic Systems With Markovian Switching , 2011, IEEE Transactions on Automatic Control.

[23]  Izumi Masubuchi,et al.  PII: S0005-1098(96)00193-8 , 2003 .

[24]  Weihai Zhang,et al.  New results on stability of singular stochastic Markov jump systems with state‐dependent noise , 2015, 1509.01102.

[25]  Li Sheng,et al.  Some remarks on stability of stochastic singular systems with state-dependent noise , 2015, Autom..

[26]  S. Campbell.  Singular systems of differential equations II , 1980 .

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

[28]  E. Uezato,et al.  Strict LMI conditions for stability, robust stabilization, and H/sub /spl infin// control of descriptor systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[29]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.