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Stability and Completion of Zeno Equilibria in Lagrangian Hybrid Systems

Or, Yizhar and Ames, Aaron D. (2011) Stability and Completion of Zeno Equilibria in Lagrangian Hybrid Systems. IEEE Transactions on Automatic Control, 56 (6). pp. 1322-1336. ISSN 0018-9286. https://resolver.caltech.edu/CaltechAUTHORS:20190204-092954756

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Abstract

This paper studies Lagrangian hybrid systems, which are a special class of hybrid systems modeling mechanical systems with unilateral constraints that are undergoing impacts. This class of systems naturally display Zeno behavior-an infinite number of discrete transitions that occur in finite time, leading to the convergence of solutions to limit sets called Zeno equilibria. This paper derives simple conditions for stability of Zeno equilibria. Utilizing these results and the constructive techniques used to prove them, the paper introduces the notion of a completed hybrid system which is an extended hybrid system model allowing for the extension of solutions beyond Zeno points. A procedure for practical simulation of completed hybrid systems is outlined, and conditions guaranteeing upper bounds on the incurred numerical error are derived. Finally, we discuss an application of these results to the stability of unilaterally constrained motion of mechanical systems under perturbations that violate the constraint.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TAC.2010.2080790DOIArticle
http://resolver.caltech.edu/CaltechCDSTR:2008.002Related ItemTechnical Report
http://resolver.caltech.edu/CaltechAUTHORS:20190226-103320953Related ItemConference Paper
Additional Information:© 2010 IEEE. Manuscript received December 30, 2008; revised September 03, 2009; accepted August 28, 2010. Date of publication September 27, 2010; date of current version June 08, 2011. This work was supported by a Fulbright Postdoctoral Fellowship and Bikura Scholarship of the Israeli Science Foundation.
Funders:
Funding AgencyGrant Number
Fulbright FoundationUNSPECIFIED
Israel Science FoundationUNSPECIFIED
Subject Keywords:Langrangian hybrid systems, stability, unilateral contact constraints, Zeno behavior
Issue or Number:6
Record Number:CaltechAUTHORS:20190204-092954756
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190204-092954756
Official Citation:Y. Or and A. D. Ames, "Stability and Completion of Zeno Equilibria in Lagrangian Hybrid Systems," in IEEE Transactions on Automatic Control, vol. 56, no. 6, pp. 1322-1336, June 2011. doi: 10.1109/TAC.2010.2080790
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92618
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Feb 2019 17:46
Last Modified:03 Oct 2019 20:46

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