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 non-autonomous
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 MD-2009 Chisinau, Moldova email: cheban@usm.md |
Return to the EJDE web page