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A Numerical Technique for Stability Analysis of Linear Switched Systems

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Hybrid Systems: Computation and Control (HSCC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2993))

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Abstract

In this paper the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms. The technique can be used to prove the stability of switched linear systems, classes of linear time-varying systems and Linear Differential Inclusions. We also present preliminary results on another related problem; namely, the construction of multiple polyhedral Lyapunov functions for specifying the existence of stabilising switching sequences.

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Author information

Authors and Affiliations

  1. Hamilton Institute, NUI, Maynooth, Ireland

    Christos A. Yfoulis & Robert Shorten

Authors
  1. Christos A. Yfoulis
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  2. Robert Shorten
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Editor information

Editors and Affiliations

  1. University of Pennsylvania,  

    Rajeev Alur

  2. School of Engineering and Applied Science, University of Pennsylvania,  

    George J. Pappas

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© 2004 Springer-Verlag Berlin Heidelberg

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Yfoulis, C.A., Shorten, R. (2004). A Numerical Technique for Stability Analysis of Linear Switched Systems. In: Alur, R., Pappas, G.J. (eds) Hybrid Systems: Computation and Control. HSCC 2004. Lecture Notes in Computer Science, vol 2993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24743-2_42

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  • DOI: https://doi.org/10.1007/978-3-540-24743-2_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21259-1

  • Online ISBN: 978-3-540-24743-2

  • eBook Packages: Springer Book Archive

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