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Discrete Dynamics in Nature and Society
Volume 2010, Article ID 408105, 19 pages
Research Article

Robust Stability Analysis and Synthesis for Switched Discrete-Time Systems with Time Delay

School of Electrical and Control Engineering, Beijing University of Technology, Chaoyang District, Beijing 100124, China

Received 24 February 2010; Revised 24 June 2010; Accepted 18 July 2010

Academic Editor: Leonid Shaikhet

Copyright © 2010 Liguo Zhang 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.


The problems of robust stability analysis and synthesis for a class of uncertain switched time-delay systems with polytopic type uncertainties are addressed. Based on the constructive use of an appropriate switched Lyapunov function, sufficient linear matrix inequalities (LMIs) conditions are investigated to make such systems a uniform quadratic stability with an -gain smaller than a given constant level. System synthesis is to design switched feedback schemes, whether based on state, output measurements, or by using dynamic output feedback, to guarantee that the corresponding closed-loop system satisfies the LMIs conditions. Two numerical examples are provided that demonstrate the efficiency of this approach.