American Journal of Applied Sciences

Stability of Non-Neutral and Neutral Dynamic Switched Systems Subject to Internal Delays

M. De la Sen, J. L. Malaina, A. Gallego and J. C. Soto

DOI : 10.3844/ajassp.2005.1481.1490

American Journal of Applied Sciences

Volume 2, Issue 10

Pages 1481-1490

Abstract

This study deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky-Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique) stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems.

Copyright

© 2005 M. De la Sen, J. L. Malaina, A. Gallego and J. C. Soto. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.