Delay-dependent H-infinity control for linear descriptor systems with delay in state

A delay-dependent H-infinity control for descriptor systems with a state-delay is investigated. The purpose of the problem is to design a linear memoryless state-feedback controller such that the resulting closed-loop system is regular, impulse free and stable with an H-infinity norm bound. Firstly, a delay-dependent bounded real lemma(BRL) of the time-delay descriptor systems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor model transformation of the system and by taking a new Lyapunov-Krasovsii functional. The introduced functional does not require bounding for cross terms, so it has less conservation.Secondly, with the help of the obtained bounded real lemma, a sufficient condition for the existence of a new delay-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrix inequalities and the solvability of the problem can be obtained by using an iterative algorithm involving convex optimization. Finally, numerical examples are given to demonstrate the effectiveness of the new method presented.

[1]  Robert K. Brayton,et al.  Small-signal stability criterion for electrical networks containing lossless transmission lines , 1968 .

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

[3]  K. Takaba,et al.  H_∞ control for descriptor systems:A J-spectral factorization approach , 1994 .

[4]  I. Masubuchi,et al.  H∞ control for descriptor systems: A matrix inequalities approach , 1997, Autom..

[5]  A. Halanay,et al.  Stability radii for some propagation models , 1997 .

[6]  Myung Jin Chung,et al.  An LMI approach to H∞ controller design for linear time-delay systems , 1997, Autom..

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

[8]  J. Lam,et al.  Delay-dependent robust H∞ control for uncertain systems with time-varying delays , 1998 .

[9]  Xi Li,et al.  Delay-dependent robust H control of uncertain linear state-delayed systems , 1999, Autom..

[10]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[11]  Wook Hyun Kwon,et al.  Delay-dependent robust H/sub /spl infin// control for uncertain systems with time-varying state-delay , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[13]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .

[14]  Necati Özdemir,et al.  State-space solutions to standard H? control problem , 2002 .

[15]  E. Fridman.  Stability of linear descriptor systems with delay: a Lyapunov-based approach , 2002 .

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