H/sub /spl infin// control of linear uncertain time-delay systems-a projection approach

The issues of stability and H/sub /spl infin// control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finsler's projection lemma, delay-dependent sufficient conditions are obtained, in terms of linear matrix inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H/sub /spl infin// state-feedback control.

[1]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[2]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[3]  Jean-Pierre Richard,et al.  Stability of some linear systems with delays , 1999, IEEE Trans. Autom. Control..

[4]  Zhou Luan-jie,et al.  Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems , 2004 .

[5]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

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

[7]  Emilia Fridman,et al.  Parameter dependent stability and stabilization of uncertain time-delay systems , 2003, IEEE Trans. Autom. Control..

[8]  Isabelle Queinnec,et al.  Delay-independent robust stability conditions of neutral linear time-delay systems , 2003 .

[9]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

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

[11]  J. Hale.  Functional Differential Equations , 1971 .

[12]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[13]  D. Mehdi,et al.  Stability and stabilizability of dynamicalsystems with multiple time-varying delays:delay-dependent criteria , 2003 .

[14]  Pierre Apkarian,et al.  Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations , 2001, IEEE Trans. Autom. Control..

[15]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[16]  Alain Bensoussan,et al.  Representation and Control of Infinite Dimensional Systems, 2nd Edition , 2007, Systems and control.

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

[18]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[19]  Rein Luus,et al.  Simultaneous stabilization of linear single-input systems by linear state feedback control , 1991 .

[20]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[21]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in System and Control Theory , 1994, Studies in Applied Mathematics.