POSITIVE FORMS AND STABILITY OF LINEAR TIME-DELAY SYSTEMS

被引：61

作者：

Peet, Matthew M. ^{[1
]}

Papachristodoulou, Antonis ^{[2
]}

Lall, Sanjay ^{[3
]}

机构：

[1] IIT, Dept Mech Mat & Aerosp Engn, Chicago, IL 60616 USA

[2] Univ Oxford, Dept Engn Sci, Oxford OX1 3PJ, England

[3] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2009年 / 47卷 / 06期

关键词：

Lyapunov stability; delay systems; semidefinite programming; OPTIMIZATION; POLYNOMIALS;

D O I：

10.1137/070706999

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit parameterization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program.

引用

页码：3237 / 3258

页数：22

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