On the Stability of Zeno Equilibria

  • Aaron D. Ames
  • Paulo Tabuada
  • Shankar Sastry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)

Abstract

Zeno behaviors are one of the (perhaps unintended) features of many hybrid models of physical systems. They have no counterpart in traditional dynamical systems or automata theory and yet they have remained relatively unexplored over the years. In this paper we address the stability properties of a class of Zeno equilibria, and we introduce a necessary paradigm shift in the study of hybrid stability. Motivated by the peculiarities of Zeno equilibria, we consider a form of asymptotic stability that is global in the continuous state, but local in the discrete state. We provide sufficient conditions for stability of these equilibria, resulting in sufficient conditions for the existence of Zeno behavior.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Aaron D. Ames
    • 1
  • Paulo Tabuada
    • 2
  • Shankar Sastry
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of California at BerkeleyBerkeleyUSA
  2. 2.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA

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