On quadratic Lyapunov functions

被引：137

作者：

Cheng, DZ ^{[1
]}

Guo, L

Huang, J

机构：

[1] Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China

[2] Chinese Univ Hong Kong, Dept Automat & Comp Aided Engn, Hong Kong, Hong Kong, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2003年 / 48卷 / 05期

关键词：

common quadratic Lyapunov function (QLF); stabilization; switched system;

D O I：

10.1109/TAC.2003.811274

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 topological structure, as a subset of [0, 2pi)(L) x R-+(n-1), is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral. The structure and the conditions are considerably simplified for planar systems. It is also proved that a set of block upper triangular matrices share a common QLF, iff each set of diagonal blocks share a common QLF.

引用

页码：885 / 890

页数：6

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