Observer‐based H ∞  control on nonhomogeneous Markov jump systems with nonlinear input

This paper considers the problem of observer‐based H ∞  controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H ∞  performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  Stability , 1973 .

[2]  D. Sworder,et al.  Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria , 1975 .

[3]  W. L. Koning,et al.  Discrete-time Markovian jump linear systems , 1993 .

[4]  E. Boukas,et al.  H∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty , 1997 .

[5]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[6]  Vasile Dragan,et al.  Control of singularly perturbed systems with Markovian jump parameters: an Hinfinity approach , 1999, Autom..

[7]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[8]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[9]  Zongli Lin,et al.  Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[10]  El-Kébir Boukas,et al.  Stochastic Switching Systems: Analysis and Design , 2005 .

[11]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[12]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[13]  Fuchun Sun,et al.  Controller design for Markov jumping systems subject to actuator saturation , 2006, Autom..

[14]  E. Boukas,et al.  Robust control of uncertain discrete-time Markovian jump systems with actuator saturation , 2006 .

[15]  E. Boukas,et al.  Mode-dependent Hºº filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. , 2007 .

[16]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[17]  Lixian Zhang,et al.  Mode-dependent Hinfinity filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[18]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[19]  Peng Shi,et al.  Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time , 2009, IEEE Transactions on Automatic Control.

[20]  E. Boukas,et al.  H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities , 2009 .

[21]  Jinliang Liu,et al.  H∞ filtering for Markovian jump systems with time-varying delays , 2010, 2010 Chinese Control and Decision Conference.

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

[23]  Fei Liu,et al.  Gain-Scheduled Robust Fault Detection on Time-Delay Stochastic Nonlinear Systems , 2011, IEEE Transactions on Industrial Electronics.

[24]  Zhenting Hou,et al.  MARKOV SKELETON PROCESS APPROACH TO A CLASS OF PARTIAL DIFFERENTIAL-INTEGRAL EQUATION SYSTEMS ARISING IN OPERATIONS RESEARCH , 2011 .

[25]  Samir Aberkane,et al.  Stochastic stabilization of a class of nonhomogeneous Markovian jump linear systems , 2011, Syst. Control. Lett..

[26]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[27]  Fei Liu,et al.  Gain-scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities , 2011, J. Frankl. Inst..

[28]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[30]  Tzuu-Hseng S. Li,et al.  OBSERVER-BASED ADAPTIVE FUZZY ROBUST CONTROLLER WITH SELF-ADJUSTED MEMBERSHIP FUNCTIONS FOR A CLASS OF UNCERTAIN MIMO NONLINEAR SYSTEMS: A PSO-SA METHOD , 2012 .

[31]  Shaocheng Tong,et al.  OBSERVER-BASED ADAPTIVE FUZZY BACKSTEPPING CONTROL FOR STRICT-FEEDBACK STOCHASTIC NONLINEAR SYSTEMS WITH TIME DELAYS , 2012 .