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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 929503, 16 pages
http://dx.doi.org/10.1155/2012/929503
Research Article

Control with Finite-Time Stability for Switched Systems under Asynchronous Switching

1Institute of National Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China
2School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Received 19 July 2012; Revised 23 September 2012; Accepted 23 September 2012

Academic Editor: Hamid Reza Karimi

Copyright © 2012 Ronghao Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the problem of controller design for switched systems under asynchronous switching with exogenous disturbances. The attention is focused on designing the feedback controller that guarantees the finite-time bounded and finite-time stability of the dynamic system. Firstly, when there exists asynchronous switching between the controller and the system, a sufficient condition for the existence of stabilizing switching law for the addressed switched system is derived. It is proved that the switched system is finite-time stabilizable under asynchronous switching satisfying the average dwell-time condition. Furthermore, the problem of control for switched systems under asynchronous switching is also investigated. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.