Non-fragile observer-based passive control for descriptor systems with time-delay

This paper investigates the problem of non-fragile observer-based passive control for descriptor systems with time-delay. The perturbations in both the control gain and observer gain of the observer-based controller are considered. For the cases of the additive perturbations and multiplicative perturbations, sufficient conditions are given such that the closed-loop systems are admissible and passive with dissipation η. The observer-based controller gains could be obtained from the solutions of linear matrix inequalities (LMIs). Moreover, the maximum dissipation of the system is provided. Simulation examples are given to show the effectiveness of the deign methods.

[1]  P. Dorato,et al.  Non-fragile controller design: an overview , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[2]  Emilia Fridman,et al.  On delay-dependent passivity , 2002, IEEE Trans. Autom. Control..

[4]  Liu Huanbin.  State-feedback H-infinity reliable controller design for descriptor systems with controller gain variations , 2007 .

[5]  J. Lam,et al.  Non‐fragile guaranteed cost control for uncertain descriptor systems with time‐varying state and input delays , 2005 .

[6]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

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

[8]  C. Lien.  H∞ non-fragile observer-based controls of dynamical systems via LMI optimization approach , 2007 .

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

[10]  X. Ji,et al.  An LMI approach to robust H-infinity control for uncertain singular time-delay systems , 2006 .

[11]  Shengyuan Xu,et al.  Non-fragile positive real control for uncertain linear neutral delay systems , 2004, Syst. Control. Lett..

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

[13]  Kiyotsugu Takaba,et al.  H2 Output Feedback Control for Descriptor Systems , 1998, Autom..

[14]  J. Lam,et al.  Robust H∞ control for uncertain singular systems with state delay , 2003 .

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

[16]  Jiang Wei,et al.  Controllability of singular systems with control delay , 2001, Autom..

[17]  Shankar P. Bhattacharyya,et al.  Robust, fragile or optimal? , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[18]  F. Lewis.  A survey of linear singular systems , 1986 .

[19]  Guang-Hong Yang,et al.  H8 control for linear systems with additive controller gain variations , 2000 .

[20]  Kan-Lin Hsiung,et al.  Lyapunov inequality and bounded real lemma for discrete-time descriptor systems , 1999 .

[21]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[22]  Lihua Xie,et al.  Observer-based positive real control of uncertain linear systems , 1999, Autom..

[23]  C. Lien,et al.  Non-fragile observer-based controls of linear system via LMI approach , 2007 .

[24]  Li Li,et al.  Observer-based robust fuzzy control of nonlinear discrete systems with parametric uncertainties , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

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

[26]  Wei Wang,et al.  Robust passive control for uncertain singular system with state delay , 2006, 2006 American Control Conference.

[27]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .