Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 471680, 21 pages
Research Article

Robust Reliable Stabilization of Switched Nonlinear Systems with Time-Varying Delays and Delayed Switching

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Received 29 September 2009; Revised 18 April 2010; Accepted 11 May 2010

Academic Editor: John Burns

Copyright © 2010 Zhengrong Xiang and Qingwei Chen. 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 is concerned with the problem of robust reliable stabilization of switched nonlinear systems with time-varying delays and delayed switching is investigated. The parameter uncertainties are allowed to be norm-bounded. The switching instants of the controller experience delays with respect to those of the system. The purpose of this problem is to design a reliable state feedback controller such that, for all admissible parameter uncertainties and actuator failure, the system state of the closed-loop system is exponentially stable. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of linear matrix inequalities (LMIs).