Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 348242, 23 pages
Research Article

Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control

1College of Computer, Chongqing University, Chongqing 400030, China
2Science Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Received 15 February 2009; Revised 9 July 2009; Accepted 16 September 2009

Academic Editor: Kok Teo

Copyright © 2009 Chuandong Li and Tingwen Huang. 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.


This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient) small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.