International Workshop on Hybrid Systems: Computation and Control

HSCC 2006: Hybrid Systems: Computation and Control pp 34-48

On the Stability of Zeno Equilibria

  • Aaron D. Ames
  • Paulo Tabuada
  • Shankar Sastry
Conference paper

DOI: 10.1007/11730637_6

Volume 3927 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Ames A.D., Tabuada P., Sastry S. (2006) On the Stability of Zeno Equilibria. In: Hespanha J.P., Tiwari A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg

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