Stability analysis of planar continuous piecewise linear systems

Author

Jun Xu ; Xiaolin Huang ; Shuning Wang

Author_Institution

Dept. of Autom., Tsinghua Univ., Beijing, China

fYear

2010

fDate

June 30 2010-July 2 2010

Firstpage

2505

Lastpage

2510

Abstract

In this paper, planar continuous piecewise linear (PCPWL) systems composed of more than two linear subsystems are investigated. Instead of using Lyapunov method, we study the behavior of the PCPWL system directly to give the stability analysis. When there exist eigenvectors for the PCPWL system, the subsystem stability ensures the global stability. If there are no eigenvectors, the one-circle-gain determines the global stability. Besides, we claim that PCPWL system with three stable subsystems is always globally stable if each subsystem has distinct real eigenvalues. Simulation results illustrate the proposed stability tests.

Keywords

continuous systems; eigenvalues and eigenfunctions; piecewise linear techniques; stability; Lyapunov method; eigenvalues; eigenvectors; global stability; one-circle-gain; planar continuous piecewise linear systems; stability analysis; Automation; Bismuth; Control systems; Eigenvalues and eigenfunctions; Linear systems; Lyapunov method; Piecewise linear techniques; Stability analysis; Systems engineering and theory; Testing;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2010

Conference_Location

Baltimore, MD

ISSN

0743-1619

Print_ISBN

978-1-4244-7426-4

Type

conf

DOI

10.1109/ACC.2010.5530702

Filename

5530702