Effects of small delays on stability of singularly perturbed systems

被引：149

作者：

Fridman, E ^{[1
]}

机构：

[1] Tel Aviv Univ, Dept Elect Engn, IL-69978 Tel Aviv, Israel

来源：

AUTOMATICA | 2002年 / 38卷 / 05期

关键词：

time-delays; singular perturbations; LMI; stability;

D O I：

10.1016/S0005-1098(01)00265-5

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A small delay in the feedback loop of a singularly perturbed system may destabilize it; however, without the delay, it is stable for all small enough values of a singular perturbation parameter e. Sufficient and necessary conditions for preserving stability, for all small enough values of delay and c, are obtained in two cases: in the case of delay proportional to e and in the case of independent delay and B. In the second case, the sufficient conditions are given in terms of an LMI. A delay-dependent LMI criterion for the stability of singularly perturbed differential-difference systems is derived. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：897 / 902

页数：6

共 19 条

[1] Delay-dependent robust H∞ control of uncertain linear state-delayed systems [J].

de Souza, CE ;

Li, X .

AUTOMATICA, 1999, 35 (07) :1313-1321

[2]

Elsgolts L. E., 1973, MATH SCI ENG, V105

[3] H∞-state-feedback control of linear systems with small state delay [J].

Fridman, E ;

Shaked, U .

SYSTEMS & CONTROL LETTERS, 1998, 33 (03) :141-150

[4]

Fridman E, 1996, Z ANGEW MATH MECH, V76, P201

[5]

FRIDMAN E, 2001, UNPUB J MATH ANAL AP

[6] H∞ control of linear singularly perturbed systems with small state delay [J].

Glizer, VY ;

Fridman, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 250 (01) :49-85

[7]

HALE J, 1999, WS528 VRIJE U AMSTER

[8]

Hale J. K., 1993, INTRO FUNCTIONAL DIF, DOI 10.1007/978-1-4612-4342-7

[9] CRITICAL CASES FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS [J].

HALE, JK .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1971, 10 (01) :59-&

[10] STABLE CENTER-STABLE CENTER CENTER-UNSTABLE UNSTABLE MANIFOLDS [J].

KELLEY, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1967, 3 (04) :546-&

← 1 2 →