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Sufficient Conditions for the Existence of Zeno Behavior

Ames, Aaron D. and Abate, Alessandro and Sastry, Shankar (2005) Sufficient Conditions for the Existence of Zeno Behavior. In: Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference. IEEE , Piscataway, NJ, pp. 696-701. ISBN 0-7803-9568-9. https://resolver.caltech.edu/CaltechAUTHORS:20190305-074933127

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Abstract

In this paper, sufficient conditions for the existence of Zeno behavior in a class of hybrid systems are given; these are the first sufficient conditions on Zeno of which the authors are aware for hybrid systems with nontrivial dynamics. This is achieved by considering a class of hybrid systems termed diagonal first quadrant (DFQ) hybrid systems. When the underlying graph of a DFQ hybrid system has a cycle, we can construct an in finite execution for this system when the vector fields on each domain satisfy certain assumptions. To this execution, we can associate a single discrete time dynamical system that describes its continuous evolution. Therefore, we reduce the study of executions of DFQ hybrid systems to the study of a single discrete time dynamical system. We obtain sufficient conditions for the existence of Zeno by determining when this discrete time dynamical system is exponentially stable.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.2005.1582237DOIArticle
ORCID:
AuthorORCID
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2005 IEEE. This research is supported by the National Science Foundation (NSF award number CCR-0225610).
Funders:
Funding AgencyGrant Number
NSFCCR-0225610
Record Number:CaltechAUTHORS:20190305-074933127
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190305-074933127
Official Citation:A. D. Ames, A. Abate and S. Sastry, "Sufficient Conditions for the Existence of Zeno Behavior," Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 2005, pp. 696-701. doi: 10.1109/CDC.2005.1582237
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93514
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Mar 2019 15:56
Last Modified:03 Oct 2019 20:55

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