Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 543145, 28 pages
doi:10.1155/2008/543145
Research Article
Stability Results for Switched Linear Systems with Constant Discrete Delays
1Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644, 48080 Bilbao, Spain
2Department of Telecommunication and Systems Engineering, Engineering School, Autonomous University of Barcelona, Cerdanyola del Vallés, Bellaterra, 08193 Barcelona, Spain
Received 11 June 2008; Revised 27 August 2008; Accepted 11 November 2008
Academic Editor: Tamas Kalmar-Nagy
Copyright © 2008 M. de la Sen and A. Ibeas. 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 investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwall's lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky-Lyapunov functional for all the above-mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time-varying systems are also discussed.