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Sufficient Conditions for Zeno Behavior in Lagrangian Hybrid Systems

Summary: Sufficient Conditions for Zeno Behavior in
Lagrangian Hybrid Systems
Andrew Lamperski and Aaron D. Ames
Control and Dynamical Systems
California Institute of Technology, Pasadena, CA 91125
Abstract. This paper presents easily verifiable sufficient conditions for
the existence of Zeno behavior in Lagrangian hybrid systems, i.e., hybrid
systems modeling mechanical systems undergoing impacts.
1 Introduction
This paper is motivated by the lack of analytic tools for proving the existence
of Zeno behavior in nontrivial hybrid systems. In particular, mechanical systems
undgergoing impacts, modeled by Lagrangian hybrid systems [3], provide a large
class of systems that often appear to display Zeno behavior. While Zeno behavior
is often intuitively clear and supported with simulation results [2], formal proofs
of Zeno behavior have been limited to very simple systems, e.g., the bouncing
To study Zeno behavior, we consider Zeno equilibria--subsets of the continu-
ous domains of a hybrid system that are fixed points of the discrete dynamics but
not the continuous dynamics--which are defined in analogy to equilibria of dy-


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


Collections: Engineering