Disturbance attenuation of uncertain switched linear systems

We study disturbance attenuation properties of switched linear systems with norm-bounded time-varying uncertainties. Based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level /spl gamma/ only by employing the largest region function strategy. This condition is constructively formulated as a bilinear matrix inequality (BMI) problem. Then the disturbance attenuation via switched state feedback is also studied. AB the switching rules adopted are constructively designed and do not depend on any uncertainties.

[1]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1998, IEEE Trans. Autom. Control..

[2]  Long Wang,et al.  Linear matrix inequality approach to quadratic stabilisation of switched systems , 2004 .

[3]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[4]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[5]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

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

[7]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[8]  Jun Zhao,et al.  Hybrid state feedback H/sub /spl infin// robust control for a class of linear systems with time-varying norm-bounded uncertainty , 2003, Proceedings of the 2003 American Control Conference, 2003..

[9]  S. Pettersson,et al.  Stabilization of hybrid systems using a min-projection strategy , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

[11]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[12]  R. Brockett,et al.  Systems with finite communication bandwidth constraints. I. State estimation problems , 1997, IEEE Trans. Autom. Control..

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

[14]  Geir E. Dullerud,et al.  H/sub /spl infin// synthesis for hybrid systems with jumps , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[15]  P. Khargonekar,et al.  STATESPACE SOLUTIONS TO STANDARD 2 H AND H? CONTROL PROBLEMS , 1989 .

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

[17]  João Pedro Hespanha,et al.  Root-mean-square gains of switched linear systems , 2003, IEEE Trans. Autom. Control..

[18]  G. Zhai,et al.  Quadratic stabilizability of switched linear systems with polytopic uncertainties , 2003 .

[19]  R. Decarlo,et al.  Asymptotic Stability of m-Switched Systems using Lyapunov-Like Functions , 1991, 1991 American Control Conference.

[20]  Guangming Xie,et al.  Quadratic stabilization of switched systems , 2005, Int. J. Syst. Sci..

[21]  S. Pettersson.  Synthesis of switched linear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[22]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[23]  J. Davenport.  Editor , 1960 .

[24]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[25]  A. Michel,et al.  Common quadratic Lyapunov-like functions with associated switching regions for two unstable second-order LTI systems , 2002 .

[26]  S. Pettersson,et al.  Hybrid system stability and robustness verification using linear matrix inequalities , 2002 .

[27]  Xinkai Chen,et al.  Stabilizing linear time-invariant systems with finite-state hybrid static output feedback , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[28]  Geir E. Dullerud,et al.  H/sub /spl infin// synthesis for multi-rate hybrid systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.