On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form

被引：118

作者：

Shorten, RN ^{[1
]}

Narendra, KS

机构：

[1] NUI Maynooth, Hamilton Inst, Maynooth, Kildare, Ireland

[2] Yale Univ, Ctr Syst Sci, New Haven, CT 06520 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2003年 / 48卷 / 04期

关键词：

quadratic stability; stability theory; switched linear systems;

D O I：

10.1109/TAC.2003.809795

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices A, and A:, are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product A(1) A(2) does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result.

引用

页码：618 / 621

页数：4

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