On the stability of zeno equilibria

Authors:
Aaron D. Ames;Paulo Tabuada;Shankar Sastry
Affiliations:
Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA;Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN;Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA
Venue:
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Year:
2006

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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.