Construction of invariant families of sets for linear systems with delay

S.V. Rakovic, R.H. Gielen, M. Lazar

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Abstract

Synthesis methods for the construction of invariant sets for delay difference equations (DDEs) suffer either from computational complexity, i.e., those based on the Krasovskii approach, or come with considerable conservatism, i.e., those based on the Razumikhin approach. This paper utilizes the concepts of vector Lyapunov functions and set-dynamics in order to introduce a novel notion of invariance for linear DDEs, termed the invariant family of sets. The proposed concept of an invariant family of sets allows for a suitable trade-off between computational simplicity and conceptual generality. In addition, it reduces the stability analysis for a DDE to the stability analysis for a relatively simple comparison system. The practical implementation for families of ellipsoidal sets proposed in this paper leads to synthesis algorithms that can be realized by solving a sequence of linear matrix inequalities.
Original languageEnglish
Title of host publicationProceedings of the American Control Conference (ACC 2012), 27-29 June 2012, Montreal, Canada
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages6246-6251
ISBN (Print)978-1-4673-2102-0
Publication statusPublished - 2012
Event2012 American Control Conference (ACC 2012) - Fairmont Queen Elizabeth, Montréal, Canada
Duration: 27 Jun 201229 Jun 2012
http://acc2012.a2c2.org/
http://acc2012.a2c2.org/index.php

Conference

Conference2012 American Control Conference (ACC 2012)
Abbreviated titleACC 2012
CountryCanada
CityMontréal
Period27/06/1229/06/12
Internet address

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    Rakovic, S. V., Gielen, R. H., & Lazar, M. (2012). Construction of invariant families of sets for linear systems with delay. In Proceedings of the American Control Conference (ACC 2012), 27-29 June 2012, Montreal, Canada (pp. 6246-6251). Institute of Electrical and Electronics Engineers.