Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.

[1]  Z. Xiang,et al.  Robust reliable stabilization of uncertain stochastic switched nonlinear systems , 2010, Proceedings of the 2010 International Conference on Modelling, Identification and Control.

[2]  Linlin Hou,et al.  Robust l2−l∞ state feedback control for uncertain discrete-time switched systems with mode-dependent time-varying delays† , 2010 .

[3]  H. Michalska,et al.  Robust stabilization of continuous-time switched linear systems , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[4]  Cheng Shao,et al.  The design of a hybrid output feedback controller for an uncertain delay system with actuator failures based on the switching method , 2010 .

[5]  Georgi M. Dimirovski,et al.  Integral Sliding Mode Control for a Class of Uncertain Switched Nonlinear Systems , 2010, Eur. J. Control.

[6]  Yingwei Zhang.  Actuator fault-tolerant control for discrete systems with strong uncertainties , 2009, Comput. Chem. Eng..

[7]  Wen-an Zhang,et al.  Stability analysis for discrete-time switched time-delay systems , 2009, Autom..

[8]  Georgi M. Dimirovski,et al.  Output feedback control for uncertain linear systems with faulty actuators based on a switching method , 2009 .

[9]  Zhengrong Xiang,et al.  Robust L∞ reliable control for uncertain nonlinear switched systems with time delay , 2009, Appl. Math. Comput..

[10]  P. Shi,et al.  Exponential H∞ filtering for switched linear systems with interval time‐varying delay , 2009 .

[11]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[12]  Grace S. Deaecto,et al.  Switched state feedback control for continuous-time uncertain systems , 2009, Autom..

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

[14]  E. Boukas,et al.  Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach , 2008 .

[15]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[16]  Long-Yeu Chung,et al.  Robust reliable Hinfinity control for uncertain nonlinear systems via LMI approach , 2008, Appl. Math. Comput..

[17]  Min Wang,et al.  Fault tolerant control of feedback linearizable systems with stuck actuators , 2008 .

[18]  Jun Zhao,et al.  On stability, L 2 -gain and H 8 control for switched systems , 2008 .

[19]  Panagiotis D. Christofides,et al.  Isolation and handling of actuator faults in nonlinear systems , 2008, at - Automatisierungstechnik.

[20]  Man Liu,et al.  Reliable H∞ control for a class of switched nonlinear systems with actuator failures , 2007 .

[21]  Peng Shi,et al.  $H_\infty$ Filtering of Discrete-Time Switched Systems With State Delays via Switched Lyapunov Function Approach , 2007, IEEE Transactions on Automatic Control.

[22]  Patrizio Colaneri,et al.  Stability and Stabilization of Continuous-Time Switched Linear Systems , 2006, SIAM J. Control. Optim..

[23]  J. Geromel,et al.  Stability and stabilization of discrete time switched systems , 2006 .

[24]  Li Yu,et al.  An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure , 2005, Appl. Math. Comput..

[25]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[26]  Panagiotis D. Christofides,et al.  Output feedback control of switched nonlinear systems using multiple Lyapunov functions , 2001, Proceedings of the 2005, American Control Conference, 2005..

[27]  Jindong Tan,et al.  A singularity-free motion control algorithm for robot manipulators - a hybrid system approach , 2004, Autom..

[28]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[29]  Richard H. Middleton,et al.  Networked control design for linear systems , 2003, Autom..

[30]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[31]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2002, IEEE Trans. Autom. Control..

[32]  Michael A. Demetriou,et al.  Adaptive reorganization of switched systems with faulty actuators , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[33]  C. Pinello,et al.  Automotive engine control and hybrid systems: challenges and opportunities , 2000, Proceedings of the IEEE.

[34]  Clyde F. Martin,et al.  A Converse Lyapunov Theorem for a Class of Dynamical Systems which Undergo Switching , 1999, IEEE Transactions on Automatic Control.

[35]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[36]  Robert J. Veillette,et al.  Reliable linear-quadratic state-feedback control , 1995, Autom..