Electron. J. Diff. Equ.,
Vol. 2010(2010), No. 21, pp. 118.
Asymptotic stability of switching systems
Driss Boularas, David Cheban
Abstract:
In this article, we study the uniform asymptotic
stability of the switched system
,
, where
is an arbitrary
piecewise constant function.
We find criteria for the asymptotic stability of nonlinear
systems. In particular, for slow and homogeneous systems,
we prove that the asymptotic stability of each individual
equation
(
)
implies the uniform asymptotic stability of the system
(with respect to switched signals).
For linear switched systems (i.e.,
, where
is a linear mapping acting on
)
we establish the following
result: The linear switched system is uniformly asymptotically stable
if it does not admit nontrivial bounded full trajectories and
at least one of the equations
is asymptotically stable.
We study this problem in the framework of linear nonautonomous
dynamical systems (cocyles).
Submitted December 21, 2009. Published February 2, 2010.
Math Subject Classifications: 34A37, 34D20, 34D23, 34D45, 37B55, 37C75, 93D20.
Key Words: Uniform asymptotic stability; cocycles; globalattractors;
uniform exponential stability; switched systems.
Show me the PDF file (341 KB),
TEX file, and other files for this article.

Driss Boularas
Xlim, UMR 6090, DMI, Faculté de Sciences
Université de Limoges
123, Avenue A. Thomas
87060, Limoges, France
email: driss.boularas@unilim.fr


David Cheban
State University of Moldova
Department of Mathematics and Informatics
A. Mateevich Street 60
MD2009 Chisinau, Moldova
email: cheban@usm.md

Return to the EJDE web page