New results on linear parameter-varying time-delay systems

Abstract A class of linear parameter-varying time-delay systems where the state-space matrices depend on time-varying parameters and the time-delay is unknown but bounded is considered. Both notions of quadratic stability (using a single quadratic Lyapunov–Krasovskii function) and affine quadratic stability (using parameter-dependent Lyapunov–Krasovskii functions) are investigated. LMI-based delay-independent and delay-dependent conditions are derived for stability testing. Then, state-feedback controllers are designed which guarantee quadratic stability and an induced L 2 -norm bound. We use a parameter-independent quadratic Lyapunov–Krasovskii function for the case of dynamic output feedback control to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set. Numerical examples are presented.

[1]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[2]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[3]  Henryk Górecki,et al.  Analysis and Synthesis of Time Delay Systems , 1989 .

[4]  Ian R. Petersen,et al.  Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems , 1997 .

[5]  Mitsuji Sampei,et al.  An algebraic approach to H ∞ output feedback control problems , 1990 .

[6]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[7]  M. F. Hassan,et al.  Decentralized structures for stream water quality control problems , 1985 .

[8]  B. Anderson,et al.  A first prin-ciples solution to the nonsingular H control problem , 1991 .

[9]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[10]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[11]  Magdi S. Mahmoud.  Dynamic control of systems with variable state-delay , 1996 .

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

[13]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions for real parametric uncertainty , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  ApkarianPierre,et al.  Self-scheduled H control of linear parameter-varying systems , 1995 .

[15]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[16]  J. S. Luo,et al.  Independent of delay stability criteria for uncertain linear state space models , 1997, Autom..

[17]  M. Mahmoud,et al.  H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities , 1999 .