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Sufficient Conditions for the Existence of Zeno Behavior
Aaron Ames, Alessandro Abate, Shankar Sastry

Citation
Aaron Ames, Alessandro Abate, Shankar Sastry. "Sufficient Conditions for the Existence of Zeno Behavior". IEEE Conference on Decision and Control, December, 2005.

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 {\em diagonal first quadrant (DFQ) hybrid systems}. When the underlying graph of a DFQ hybrid system has a cycle, we can construct an infinite 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.

 Citation formats
• HTML
Aaron Ames, Alessandro Abate, Shankar Sastry. <a
href="http://chess.eecs.berkeley.edu/pubs/131.html"
>Sufficient Conditions for the Existence of Zeno
Behavior</a>, IEEE Conference on Decision and Control,
December, 2005.
• Plain text
Aaron Ames, Alessandro Abate, Shankar Sastry.
"Sufficient Conditions for the Existence of Zeno
Behavior". IEEE Conference on Decision and Control,
December, 2005.
• BibTeX
@inproceedings{AmesAbateSastry05_SufficientConditionsForExistenceOfZenoBehavior,
author = {Aaron Ames and Alessandro Abate and Shankar Sastry},
title = {Sufficient Conditions for the Existence of Zeno
Behavior},
booktitle = {IEEE Conference on Decision and Control},
month = {December},
year = {2005},
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 {\em diagonal first quadrant (DFQ)
hybrid systems}. When the underlying graph of a
DFQ hybrid system has a cycle, we can construct an
infinite 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.},
URL = {http://chess.eecs.berkeley.edu/pubs/131.html}
}


Posted by Aaron Ames on 15 May 2006.
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