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On the Existence of Zeno Behavior in Hybrid Systems with Non-Isolated Zeno Equilibria
 

Summary: On the Existence of Zeno Behavior in Hybrid Systems with Non-Isolated
Zeno Equilibria
Andrew Lamperski and Aaron D. Ames
Abstract-- This paper presents proof-certificate based suffi-
cient conditions for the existence of Zeno behavior in hybrid
systems near non-isolated Zeno equilibria. To establish these
conditions, we first prove sufficient conditions for Zeno behavior
in a special class of hybrid systems termed first quadrant interval
hybrid systems. The proof-certificate sufficient conditions are
then obtained through a collection of functions that effectively
"reduce" a general hybrid system to a first quadrant interval
hybrid system. This paper concludes with an application of
these ideas to Lagrangian hybrid systems, resulting in easily
verifiable sufficient conditions for Zeno behavior.
I. INTRODUCTION
This paper was motivated by the lack of analytic tools for
proving the existence of Zeno behavior in nontrivial hybrid
systems. In particular, mechanical systems undgergoing im-
pacts, modeled by Lagrangian hybrid systems [1], provide
a large class of systems that often appear to display Zeno

  

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

 

Collections: Engineering