Stability of singularly perturbed functional-differential systems: spectrum analysis and LMI approaches

被引：12
作者：
Glizer, Valery Y. [1 ]
Fridman, Emilia [2 ]
机构：
[1] Ort Braude Coll, Dept Math, IL-21982 Karmiel, Israel
[2] Tel Aviv Univ, Dept Elect Engn Syst, IL-69978 Tel Aviv, Israel
来源：
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION | 2012年 / 29卷 / 01期
基金：
以色列科学基金会;
关键词：
functional-differential system; singular perturbation; exponential stability; spectrum analysis; linear matrix inequality; H-INFINITY CONTROL; SMALL DELAYS; STABILIZATION; STATE;
D O I：
10.1093/imamci/dnr027
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 singularly perturbed linear functional-differential system is considered. The delay is assumed to be small of the order of a small parameter multiplying a part of derivatives in the system. It is `not assumed that the fast subsystem is asymptotically stable'. Two approaches to the study of the exponential stability of the singularly perturbed system are suggested. The first one treats systems with constant delays via the analysis of asymptotic behaviour of the roots of their characteristic equation. The second approach develops a direct Lyapunov-Krasovskii method for systems with time-varying delays leading to stability conditions in terms of linear matrix inequalities. Numerical examples illustrate the efficiency of both approaches.
引用
收藏
页码：79 / 111
页数：33
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