CUED Publications database

Lyapunov theory for zeno stability

Lamperski, A and Ames, AD (2013) Lyapunov theory for zeno stability. IEEE Transactions on Automatic Control, 58. pp. 100-112. ISSN 0018-9286

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Abstract

Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood. The goal of this paper is to develop a stability theory for Zeno hybrid systems that parallels classical Lyapunov theory; that is, we present Lyapunov-like sufficient conditions for Zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler Zeno hybrid systems defined on the first quadrant of the plane. These conditions are applied to Lagrangian hybrid systems, which model mechanical systems undergoing impacts, yielding simple sufficient conditions for Zeno behavior. Finally, the results are applied to robotic bipedal walking. © 2012 IEEE.

Item Type: Article
Uncontrolled Keywords: Hybrid systems Lyapunov method mechanical systems stability
Subjects: UNSPECIFIED
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:26
Last Modified: 08 Dec 2014 02:31
DOI: 10.1109/TAC.2012.2208292