On quadratic Lyapunov functions

被引：139
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.
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页码：885 / 890
页数：6
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