Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 315713, 28 pages
Research Article

Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control

1Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa (Bizkaia), Aptdo, 644-Bilbao, Spain
2Department of Telecommunication and Systems Engineering, Engineering School, Autonomous University of Barcelona, Cerdanyola del Vallés, Bellaterra, 08193 Barcelona, Spain

Received 6 November 2008; Revised 5 March 2009; Accepted 24 March 2009

Academic Editor: Antonia Vecchio

Copyright © 2009 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.


This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.