Delay-dependent robust stabilization of uncertain systems with multiple state delays

This paper deals with the problem of robust stabilization for uncertain systems with multiple state delays. The parameter uncertainties are time-varying and unknown but are norm-bounded, and the delays are time-varying. A new method for achieving robust stabilization is presented for a class of uncertain time-delay systems via linear memoryless state feedback control. The results depend on the size of the delays and are given in terms of several linear matrix inequalities.

[1]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[2]  M. Ikeda,et al.  Stabilization of linear systems with time-varying delay , 1979 .

[3]  S. Żak,et al.  On stability independent of delay for linear systems , 1982 .

[4]  Ian R. Petersen,et al.  A riccati equation approach to the stabilization of uncertain linear systems , 1986, Autom..

[5]  W. Schmitendorf.  Designing stabilizing controllers for uncertain systems using the Riccati equation approach , 1988 .

[6]  S. Gutman,et al.  Stabilization of uncertain dynamic systems including state delay , 1989 .

[7]  H. Kokame,et al.  Stability of x(t)=Ax(t)+Bx(t- tau ) , 1989 .

[8]  Faryar Jabbari,et al.  A noniterative method for the design of linear robust controllers , 1990 .

[9]  Bor-Sen Chen,et al.  Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach , 1991 .

[10]  K. Furuta,et al.  Memoryless stabilization of uncertain linear systems including time-varying state delays , 1992 .

[11]  T. Su,et al.  Robust stability of delay dependence for linear uncertain systems , 1992 .

[12]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[13]  Bugong Xu.  Comments on "Robust stability of delay dependence for linear uncertain systems" , 1994 .

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

[15]  Juing-Huei Su.  Further results on the robust stability of linear systems with a single time delay , 1994 .

[16]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

[17]  C. de Souza,et al.  LMI approach to delay-dependent robust stability and stabilization of uncertain linear delay systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[18]  Y. Cao,et al.  Robust stabilization of uncertain multi-state-delay systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

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

[20]  Y. Cao,et al.  Robust stabilization of uncertain systems with time-varying multistate delay , 1998, IEEE Trans. Autom. Control..