A Caltech Library Service

Characterization of Zeno behavior in hybrid systems using homological methods

Ames, Aaron D. and Sastry, Shankar (2005) Characterization of Zeno behavior in hybrid systems using homological methods. In: 2005 American Control Conference. IEEE , Piscataway, NJ, pp. 1160-1165. ISBN 0-7803-9098-9.

[img] PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


It is possible to associate to a hybrid system a single topological space its underlying topological space. Simultaneously, every hybrid system has a graph as its indexing object its underlying graph. Here we discuss the relationship between the underlying topological space of a hybrid system, its underlying graph and Zeno behavior. When each domain is contractible and the reset maps are homotopic to the identity map, the homology of the underlying topological space is isomorphic to the homology of the underlying graph; the nonexistence of Zeno is implied when the first homology is trivial. Moreover, the first homology is trivial when the null space of the incidence matrix is trivial. The result is an easy way to verify the nonexistence of Zeno behavior.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2005 AACC. This research is supported by the National Science Foundation (NSF award number CCR-0225610).
Funding AgencyGrant Number
Record Number:CaltechAUTHORS:20190304-152359371
Persistent URL:
Official Citation:A. D. Ames and S. Sastry, "Characterization of Zeno behavior in hybrid systems using homological methods," Proceedings of the 2005, American Control Conference, 2005., Portland, OR, USA, 2005, pp. 1160-1165 vol. 2. doi: 10.1109/ACC.2005.1470118
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93476
Deposited By: Tony Diaz
Deposited On:04 Mar 2019 23:27
Last Modified:16 Nov 2021 16:58

Repository Staff Only: item control page