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Sufficient conditions for the existence of Zeno behavior in a class of nonlinear hybrid systems via constant approximations

Ames, Aaron D. and Abate, Alessandro and Sastry, Shankar (2008) Sufficient conditions for the existence of Zeno behavior in a class of nonlinear hybrid systems via constant approximations. In: 46th IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 5420-5425. ISBN 978-1-4244-1497-0 . https://resolver.caltech.edu/CaltechAUTHORS:20100813-134422032

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Abstract

The existence of Zeno behavior in hybrid systems is related to a certain type of equilibria, termed Zeno equilibria, that are invariant under the discrete, but not the continuous, dynamics of a hybrid system. In analogy to the standard procedure of linearizing a vector field at an equilibrium point to determine its stability, in this paper we study the local behavior of a hybrid system near a Zeno equilibrium point by considering the value of the vector field on each domain at this point, i.e., we consider constant approximations of nonlinear hybrid systems. By means of these constant approximations, we are able to derive conditions that simultaneously imply both the existence of Zeno behavior and the local exponential stability of a Zeno equilibrium point. Moreover, since these conditions are in terms of the value of the vector field on each domain at a point, they are remarkably easy to verify.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/CDC.2007.4434891 DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4434891PublisherUNSPECIFIED
ORCID:
AuthorORCID
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2007 IEEE.
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INSPEC Accession Number9885989
Record Number:CaltechAUTHORS:20100813-134422032
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100813-134422032
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19430
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Aug 2010 21:34
Last Modified:03 Oct 2019 01:56

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