H/sub /spl infin// output feedback control for descriptor systems with delayed-state

Using the method of linear matrix inequalities (LMI), this paper considers the H/sub /spl infin// dynamic output feedback control for descriptor systems with delayed-state. The controller is one descriptor system without delay. Several equivalent sufficient conditions for the existence of one descriptor dynamic controller without impulsive models are given. Furthermore the explicit expression of the desired controller is obtained. Finally one example is given to show the validity of the proposed results.

[1]  Christopher I. Byrnes,et al.  Output regulation for nonlinear systems: an overview , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[2]  D. Luenberger,et al.  SINGULAR DYNAMIC LEONTIEF SYSTEMS1 , 1977 .

[3]  F. Jun-e,et al.  Guaranteed cost control of linear uncertain singular time-delay systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[4]  Jang Gyu Lee,et al.  Robust stability and stabilization of linear delayed systems with structured uncertainty , 1999, Autom..

[5]  Jian Chu,et al.  Stabilization of a class of uncertain time-delay systems containing saturating actuators , 1999, Int. J. Syst. Sci..

[6]  J. Lam,et al.  Robust D-stability analysis for uncertain discrete singular systems with state delay , 2002 .

[7]  F. Jun-e,et al.  Singular linear-quadratic optimal control problem for a class of discrete singular systems with multiple time-delays , 2003 .

[8]  Uri M. Ascher,et al.  The numerical solution of delay-differential-algebraic equations of retarded and neutral type , 1995 .

[9]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[10]  S. Campbell Singular linear systems of differential equations with delays , 1980 .

[11]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[12]  Linda R. Petzold,et al.  Asymptotic stability of linear delay differential-algebraic equations and numerical methods , 1997 .

[13]  Zhaolin Cheng,et al.  Singular linear-quadratic optimal control problem for a class of discrete singular systems with multiple time-delays , 2003, Int. J. Syst. Sci..

[14]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[15]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

[16]  Naresh K. Sinha,et al.  Control Systems , 1986 .

[17]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[18]  Erik I. Verriest,et al.  On the stability of coupled delay differential and continuous time difference equations , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[19]  Myung Jin Chung,et al.  Robust observer-based H∞ controller design for linear uncertain time-delay systems , 1997, Autom..

[20]  H. Schättler,et al.  Local bifurcations and feasibility regions in differential-algebraic systems , 1995, IEEE Trans. Autom. Control..

[21]  J. Aplevich Implicit Linear Systems , 1991 .

[22]  S. Sastry,et al.  Jump behavior of circuits and systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[23]  W. Kwon,et al.  Memoryless H∞ controllers for state delayed systems , 1994, IEEE Trans. Autom. Control..