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Stability of Zeno Equilibria in Lagrangian Hybrid Systems Yizhar Or and Aaron D. Ames
 

Summary: Stability of Zeno Equilibria in Lagrangian Hybrid Systems
Yizhar Or and Aaron D. Ames
Abstract-- This paper presents both necessary and sufficient
conditions for the stability of Zeno equilibria in Lagrangian
hybrid systems, i.e., hybrid systems modeling mechanical sys-
tems undergoing impacts. These conditions for stability are
motivated by the sufficient conditions for Zeno behavior in
Lagrangian hybrid systems obtained in [11]--we show that the
same conditions that imply the existence of Zeno behavior near
Zeno equilibria imply the stability of the Zeno equilibria. This
paper, therefore, not only presents conditions for the stability
of Zeno equilibria, but directly relates the stability of Zeno
equilibria to the existence of Zeno behavior.
I. INTRODUCTION
Zeno behavior occurs in a hybrid system when an infinite
number of discrete transitions occur in a finite amount
of time. Despite the simplicity of the definition of Zeno
behavior, understanding this behavior on a fundamental level
presents difficult and intriguing problems in hybrid systems.
Can simple conditions for the existence of Zeno behavior be

  

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

 

Collections: Engineering