On a class of linear constant systems which have a common quadratic Lyapunov function

Author

Mori, Yoshihiro ; Mori, Takehiro ; Kuroe, Yasuaki

Author_Institution

Dept. of Electron. & Inf. Sci., Kyoto Inst. of Technol., Japan

Volume

3

fYear

1998

fDate

1998

Firstpage

2808

Abstract

The common Lyapunov function problem to be studied here, is to find a set of systems which have a common quadratic Lyapunov function guaranteeing asymptotic stability of its all member systems. This problem comes from diverse fields of system stability analysis. Several sets of linear systems which have a common quadratic Lyapunov function are known. But these results are still restrictive. In this paper, we provide one more new class of such systems. We first show a necessary and sufficient condition for a set of systems to have a common quadratic Lyapunov function. By using this condition and a property of M-matrices, we obtain a class of systems having a common quadratic Lyapunov function. A numerical example is presented to show that the obtained class is in fact a new one

Keywords

Lyapunov matrix equations; asymptotic stability; M-matrices; asymptotic stability; common quadratic Lyapunov function; linear constant systems; necessary and sufficient condition; system stability analysis; Asymptotic stability; Eigenvalues and eigenfunctions; Information science; Linear matrix inequalities; Linear systems; Lyapunov method; Stability analysis; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1998. Proceedings of the 37th IEEE Conference on

Conference_Location

Tampa, FL

ISSN

0191-2216

Print_ISBN

0-7803-4394-8

Type

conf

DOI

10.1109/CDC.1998.757882

Filename

757882