Research Article Open Access

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

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.

American Journal of Applied Sciences
Volume 2 No. 10, 2005, 1481-1490

DOI: https://doi.org/10.3844/ajassp.2005.1481.1490

Submitted On: 18 October 2005 Published On: 31 October 2005

How to Cite: De la Sen, M., Malaina, J. L., Gallego, A. & Soto, J. C. (2005). Stability of Non-Neutral and Neutral Dynamic Switched Systems Subject to Internal Delays. American Journal of Applied Sciences, 2(10), 1481-1490. https://doi.org/10.3844/ajassp.2005.1481.1490

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Keywords

  • Asymptotic stability
  • Quadratic stability
  • Uniform stability
  • Convexity problems
  • Uncommensurate time-delay systems
  • Neutral time- delay systems