Approximating periodic trajectories of contractive systems

Michael Margaliot*, Samuel Coogan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable periodic solution. Obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in numerous applications. We develop an approach for approximating such a periodic trajectory using the periodic trajectory of a simpler system (e.g. an LTI system). Our approximation includes an error bound that is based on the input-to-state stability property of contractive systems. We show that in some cases this error bound can be computed explicitly. We demonstrate our results using several examples from systems biology.

Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages583-588
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - 28 Jun 2017
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/TerritoryAustralia
CityMelbourne
Period12/12/1715/12/17

Funding

FundersFunder number
Israeli Ministry of Science, Technology & Space
Sagol School of Neuroscience
School of Electrical Engineering
Tel-Aviv UniversityTel-Aviv 69978
US-Israel Binational Science Foundation
Israel Science Foundation410/15

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