Exponential stability of linear distributed parameter systems with time-varying delays

被引：202

作者：

Fridman, Emilia ^{[1
]}

Orlov, Yury ^{[2
]}

机构：

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

[2] CICESE Res Ctr, Ensenada 22860, Baja California, Mexico

来源：

AUTOMATICA | 2009年 / 45卷 / 01期

关键词：

Distributed parameter systems; Time-varying delay; Stability; Lyapunov method; LMI; FUNCTIONAL-DIFFERENTIAL EQUATIONS; DEPENDENT STABILITY; LMI APPROACH; FEEDBACKS; RESPECT;

D O I：

10.1016/j.automatica.2008.06.006

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Exponential stability analysis via the Lyapunov-Krasovskii method is extended to linear time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay. Sufficient delay-dependent conditions for exponential stability are derived in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation and to a wave equation, these conditions are reduced to standard Linear Matrix Inequalities (LMIs). The proposed method is expected to provide effective tools for stability analysis and control synthesis of distributed parameter systems. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：194 / 201

页数：8

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