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On the Stability of Zeno Equilibria Aaron D. Ames1

Summary: On the Stability of Zeno Equilibria
Aaron D. Ames1
, Paulo Tabuada2
, and Shankar Sastry1
Department of Electrical Engineering and Computer Sciences
University of California at Berkeley, Berkeley, CA 94720
Department of Electrical Engineering
University of Notre Dame, Notre Dame, IN 46556
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


Source: Ames, Aaron - Department of Mechanical Engineering, Texas A&M University


Collections: Engineering