Prajna, Stephen and Jadbabaie, Ali (2005) Methods for Safety Verification of Time-Delay Systems. In: 2005 44th IEEE Conference on Decision and Control & European Control Conference. IEEE Conference on Decision and Control & European Control Conference. IEEE , Piscataway, NJ, pp. 4348-4353. ISBN 0-7803-9567-0. https://resolver.caltech.edu/CaltechAUTHORS:20110829-081539175
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Abstract
This paper addresses the safety verification of systems with time-delay. It extends the barrier certificate methodology previously proposed for safety verification of systems described by ordinary differential equations to the functional differential equations setting. For verifying the safety of a time-delay system, a functional of states is used as a barrier certificate. The forms of the functionals resemble the Lyapunov-Razumikhin functions or the Lyapunov-Krasovskii functionals used in stability analysis of time-delay systems. When the description of the system is given in terms of polynomials, such a barrier certificate can be searched using sum of squares programming.
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| Additional Information: | © 2005 IEEE. Issue Date: 12-15 Dec. 2005. Date of Current Version: 30 January 2006. The work of the first author was financially supported by the Army Institute for Collaborative Biotechnologies, the NSF Award CCF-0326635 “ITR COLLAB: Theory and Software Infrastructure for a Scalable Systems Biology,” and the AFOSR Award FA9550-05-1-0032 “Bio Inspired Networks.” The first author would also like to thank Antonis Papachristodoulou for the enlightening discussions on time delay systems. | |||||||||
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| Series Name: | IEEE Conference on Decision and Control & European Control Conference | |||||||||
| DOI: | 10.1109/CDC.2005.1582846 | |||||||||
| Record Number: | CaltechAUTHORS:20110829-081539175 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20110829-081539175 | |||||||||
| Official Citation: | Prajna, S.; Jadbabaie, A.; , "Methods for Safety Verification of Time-Delay Systems," Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on , vol., no., pp. 4348- 4353, 12-15 Dec. 2005 doi: 10.1109/CDC.2005.1582846 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1582846&isnumber=33412 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 25135 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 07 Sep 2011 14:42 | |||||||||
| Last Modified: | 09 Nov 2021 16:30 |
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