Robust Stabilization of Discrete-time Switched Uncertain Systems Subject to Actuator Saturation

The robust stabilization problem for switched uncertain systems with saturating actuators is addressed here. The systems considered are discrete-time with parametric uncertainties entering all the matrices in the system representation. A switching control law is designed and a region is specified in which the stability of the closed-loop system is ensured by using the composite Lyapunov function, and the robust controller is constructed in terms of the solution to a set of linear matrix inequalities(LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.

[1]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[2]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[3]  Long Wang,et al.  Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach , 2006 .

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

[5]  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).

[6]  O. Akhrif,et al.  Stability and control synthesis of switched systems subject to actuator saturation , 2004, Proceedings of the 2004 American Control Conference.

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

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

[9]  C. Burgat,et al.  Regulator problem for linear discrete-time systems with non-symmetrical constrained control , 1988 .

[10]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[11]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

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

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Long Wang,et al.  Quadratic stabilization of uncertain discrete-time switched linear systems , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).

[15]  Andrew R. Teel,et al.  Control of linear systems with saturating actuators , 1996 .