A NOVEL APPROACH TO EXACT SLOW-FAST DECOMPOSITION OF LINEAR SINGULARLY PERTURBED SYSTEMS WITH SMALL DELAYS

被引：18

作者：

Glizer, Valery Y. ^{[1
]}

Fridman, Emilia ^{[2
]}

Feigin, Yuri ^{[2
]}

机构：

[1] ORT Braude Coll Engn, Dept Math, IL-2161002 Karmiel, Israel

[2] Tel Aviv Univ, Sch Elect Engn, IL-69978 Tel Aviv, Israel

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2017年 / 55卷 / 01期

基金：

以色列科学基金会;

关键词：

singularly perturbed system; time delay system; small delay; exact slow-fast system decomposition; exact slow-fast spectrum decomposition; multilink single-sink optical network; stability; H-INFINITY CONTROL; EXPONENTIAL STABILITY; DIFFERENTIAL-SYSTEMS; EQUATION; MATRIX; STATE;

D O I：

10.1137/140981009

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 linear time-invariant singularly perturbed system with multiple pointwise and distributed small time delays is considered. A novel (direct) approach to exact slow-fast decomposition of this system is proposed. In contrast with the existing method, this approach uses neither a preliminary transformation of the original differential system to an integral one nor rather complicated integral manifold and operator techniques. Moreover, the approach of the present paper does not assume the exponential stability of the fast subsystem. Based on this decomposition, an exact slow-fast decomposition of the spectrum of a singularly perturbed system with a single pointwise small delay is carried out. Using the theoretical results, the stability of a multilink single-sink optical network is analyzed.

引用

页码：236 / 274

页数：39

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