Asymptotic Stability Analysis of a Kind of Switched Positive Linear Discrete Systems

Author

Xue, Xiaoping ; Li, Zhuchun

Author_Institution

Dept. of Math., Harbin Inst. of Technol., Harbin, China

Volume

55

Issue

9

fYear

2010

Firstpage

2198

Lastpage

2203

Abstract

This note studies the asymptotic stability of switched positive linear discrete systems whose subsystems are (sp) matrices. Such a matrix is the character of a kind of asymptotically stable linear systems and it is very easy to test. A new definition of (sp) matrix is given by means of graph theory. Based on an approaching using partially ordered semigroups and Lie algebras, we present several new criteria for asymptotic stability. We also derive an algebraic condition and discuss a kind of higher order difference equation. Our results have a robustness property to some extent.

Keywords

asymptotic stability; discrete systems; graph theory; linear systems; matrix algebra; asymptotic stability analysis; graph theory; switched positive linear discrete systems; Algebra; Asymptotic stability; Difference equations; Graph theory; Linear systems; Lyapunov method; Robustness; Stability analysis; Switched systems; System testing; $(sp)$ matrix; Asymptotic stability; Lie algebra; directed graph; partially ordered semigroup; saturated vertex; substochastic matrix; switched systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2052144

Filename

5482035