Stability and Completion of Zeno Equilibria in Lagrangian Hybrid Systems
- Creators
- Or, Yizhar
- Ames, Aaron D.
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.
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.Attached Files
Published - 05586645.pdf
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Additional details
- Eprint ID
- 92618
- Resolver ID
- CaltechAUTHORS:20190204-092954756
- Fulbright Foundation
- Israel Science Foundation
- Created
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2019-02-04Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field