Asymptotic stability of switching systems. (English) Zbl 1198.34012

Boularas, Driss; Cheban, David

Electron. J. Differ. Equ. 2010, Paper No. 21, 18 p. (2010).

The authors first introduce shift dynamical systems on the space of piecewise constant functions and show that every switched system generates a cocycle. Necessary and sufficient conditions for asymptotic stability of switched homogeneous systems are given, a sufficient condition for the asymptotic stability of slow switched homogeneous systems is obtained. Furthermore, the authors obtain necessary and sufficient conditions for the uniform asymptotic stability of linear switched systems.

Reviewer: Olusola Akinyele (Bowie)

MSC:

34A36	Discontinuous ordinary differential equations
34D20	Stability of solutions to ordinary differential equations
34D45	Attractors of solutions to ordinary differential equations
37B55	Topological dynamics of nonautonomous systems

Keywords:

uniform asymptotic stability; cocycles; global attractors; uniform exponential stability; switched systems