Journal of Applied Mathematics
Volume 2012 (2012), Article ID 482792, 28 pages
http://dx.doi.org/10.1155/2012/482792
Research Article

Exponential Admissibility and Control of Switched Singular Time-Delay Systems: An Average Dwell Time Approach

Jinxing Lin1,2 and Zhifeng Gao1

1College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, China
2Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing, Jiangsu 210096, China

Received 16 September 2012; Accepted 22 November 2012

Academic Editor: Jitao Sun

Copyright © 2012 Jinxing Lin and Zhifeng Gao. 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 deals with the problems of exponential admissibility and control for a class of continuous-time switched singular systems with time-varying delay. The controllers to be designed include both the state feedback (SF) and the static output feedback (SOF). First, by using the average dwell time scheme, the piecewise Lyapunov function, and the free-weighting matrix technique, an exponential admissibility criterion, which is not only delay-range-dependent but also decay-rate-dependent, is derived in terms of linear matrix inequalities (LMIs). A weighted performance criterion is also provided. Then, based on these, the solvability conditions for the desired SF and SOF controllers are established by employing the LMI technique, respectively. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach.