This article is cited in 3 papers

Differential Equations

On the Stability of Hybrid Homogeneous Systems

A. Yu. Aleksandrov, A. V. Platonov

Dept. of Medical and Biological Systems Control, Saint-Petersburg State University, Faculty of Applied Mathematics and Control Processes, Saint-Petersburg

Abstract: The hybrid system consisting of the family of subsystems with homogeneous right-hand sides and a switching law is considered. It is assumed that the zero solution of each subsystem is asymptotically stable. By the use of the Lyapunov functions method, the classes of admissible switching laws are determined under which the corresponding hybrid system is also asymptotically stable. The region of asymptotic stability of the zero solution is investigated.

Keywords: switched systems, stability, homogeneous systems, Lyapunov functions, region of asymptotic stability.

UDC: 517.977

MSC: 34A38, 34D20

Original article submitted 08/VI/2010
revision submitted – 26/VIII/2010

DOI: 10.14498/vsgtu798

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