Robust H∞ dynamic output feedback control for uncertain discrete-time switched systems with time-varying delays

In this paper, robust Hinfin output feedback control problem for a class of linear discrete-time switched systems with norm-bounded uncertainty and time-varying delay is investigated. A switched dynamic output feedback controller which robustly exponentially stabilizes the switched system and reduces the effect of the disturbance input on the controlled output to a prescribed level was constructed. By using switched Lyapunov function technique, a delay-dependent linear matrix inequality-based sufficient condition for the problem to be solvable is derived. Controller design is performed by solving a set of linear matrix inequalities. Finally, a simulation example is given to illustrate the validity of the results.

[1]  Seong-Ho Song,et al.  H∞ Control of discrete-time linear systems with norm-bounded uncertainties and time delay in state , 1998, Autom..

[2]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[3]  Z. K. Liu,et al.  STABILITY AND STABILIZABILITY OF A CLASS OF DYNAMICAL UNCERTAIN SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS , 2002 .

[4]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

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

[6]  Long Wang,et al.  Robust stability analysis and control synthesis for discrete-time uncertain switched systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  J. Bernussou,et al.  Robust dynamic output feedback control for switched systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[8]  Guang-Hong Yang,et al.  Robust controllability and robust closed-loop stability with static output feedback for a class of uncertain descriptor systems , 1999 .

[9]  G. Zhai.  Quadratic stabilizability of discrete-time switched systems via state and output feedback , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[10]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers , 2004, Syst. Control. Lett..

[11]  R. Decarlo,et al.  Construction of piecewise Lyapunov functions for stabilizing switched systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[13]  Jong Hae Kim,et al.  Hinfinity state feedback control for generalized continuous/discrete time-delay system , 1999, Autom..

[14]  Georgi M. Dimirovski,et al.  Quadratic stability of a class of switched nonlinear systems , 2004, IEEE Trans. Autom. Control..