On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria

Andrew Lamperski; Aaron D. Ames

doi:10.1109/CDC.2008.4739100

On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria

Andrew Lamperski, Aaron D. Ames

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

20 Scopus citations

Abstract

This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively "reduce" a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior.

Original language	English (US)
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2776-2781
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4739100
State	Published - 2008
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: Dec 9 2008 → Dec 11 2008

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	47th IEEE Conference on Decision and Control, CDC 2008
Country/Territory	Mexico
City	Cancun
Period	12/9/08 → 12/11/08

Publisher link

10.1109/CDC.2008.4739100

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Lamperski, A., & Ames, A. D. (2008). On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 2776-2781). Article 4739100 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4739100

On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria. / Lamperski, Andrew; Ames, Aaron D.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 2776-2781 4739100 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lamperski, A & Ames, AD 2008, On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4739100, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2776-2781, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 12/9/08. https://doi.org/10.1109/CDC.2008.4739100

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AB - This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively "reduce" a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior.

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On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria

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