An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay*

被引：387

作者：

Zhang, Xian-Ming ^{[1
]}

Han, Qing-Long ^{[1
]}

Seuret, Alexandre ^{[2
]}

Gouaisbaut, Frederic ^{[2
]}

机构：

[1] Swinburne Univ Technol, Sch Software & Elect Engn, Melbourne, Vic 3122, Australia

[2] CNRS, LAAS, 7 Ave Colonel Roche, F-31077 Toulouse, France

来源：

AUTOMATICA | 2017年 / 84卷

基金：

澳大利亚研究理事会;

关键词：

Time-delay systems; Stability; Reciprocally convex inequality; Lyapunov-Krasovskii functional; DEPENDENT STABILITY; INTEGRAL INEQUALITY; CRITERIA;

D O I：

10.1016/j.automatica.2017.04.048

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with stability of a linear system with a time-varying delay. First, an improved reciprocally convex inequality including some existing ones as its special cases is derived. Compared with an extended reciprocally convex inequality recently reported, the improved reciprocally convex inequality can provide a maximum lower bound with less slack matrix variables for some reciprocally convex combinations. Second, an augmented Lyapunov Krasovskii functional is tailored for the use of a second-order Bessel Legendre inequality. Third, a stability criterion is derived by employing the proposed reciprocally convex inequality and the augmented Lyapunov Krasovskii functional. Finally, two well studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time-varying delay than some existing criteria. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：221 / 226

页数：6

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