Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 134296, 7 pages
http://dx.doi.org/10.1155/2013/134296
Research Article

Stabilization of Discrete-Time Planar Switched Linear Systems with Impulse

Yanli Zhu1,2 and Yuangong Sun1

1School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China
2School of Automation and Electrical Engineering, University of Jinan, Jinan, Shandong 250022, China

Received 20 January 2013; Accepted 3 April 2013

Academic Editor: Hua Su

Copyright © 2013 Yanli Zhu and Yuangong Sun. 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

We study the stabilization problem of discrete-time planar switched linear systems with impulse. When all subsystems are controllable, based on an explicit estimation on the state transition matrix, we establish a sufficient condition such that the switched impulsive system is stabilizable under arbitrary switching signal with given switching frequency. When there exists at least one uncontrollable subsystem, a sufficient condition is also given to guarantee the stabilization of the switched impulsive system under appropriate switching signal.