Stability of systems with fast-varying delay using improved Wirtinger's inequality

Alexandre Seuret; Frédéric Gouaisbaut; Emilia Fridman

doi:10.1109/CDC.2013.6760004

Stability of systems with fast-varying delay using improved Wirtinger's inequality

Alexandre Seuret, Frédéric Gouaisbaut, Emilia Fridman

School of Electrical Engineering

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

105 Scopus citations

Abstract

This paper considers the stability of systems with fast-varying delay. The novelty of the paper comes from the consideration of a new integral inequality which is proved to be less conservative than the celebrated Jensen's inequality. Based on this new inequality, a dedicated construction of Lyapunov-Krasovskii functionals is proposed and is showed to have a great potential in practice. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality, recently provided in the literature, in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

Original language	English
Title of host publication	2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	946-951
Number of pages	6
ISBN (Print)	9781467357173
DOIs	https://doi.org/10.1109/CDC.2013.6760004
State	Published - 2013
Event	52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: 10 Dec 2013 → 13 Dec 2013

Publication series

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

Conference

Conference	52nd IEEE Conference on Decision and Control, CDC 2013
Country/Territory	Italy
City	Florence
Period	10/12/13 → 13/12/13

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10.1109/CDC.2013.6760004

Cite this

Seuret, A., Gouaisbaut, F., & Fridman, E. (2013). Stability of systems with fast-varying delay using improved Wirtinger's inequality. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 946-951). Article 6760004 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760004

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abstract = "This paper considers the stability of systems with fast-varying delay. The novelty of the paper comes from the consideration of a new integral inequality which is proved to be less conservative than the celebrated Jensen's inequality. Based on this new inequality, a dedicated construction of Lyapunov-Krasovskii functionals is proposed and is showed to have a great potential in practice. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality, recently provided in the literature, in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.",

author = "Alexandre Seuret and Fr{\'e}d{\'e}ric Gouaisbaut and Emilia Fridman",

year = "2013",

doi = "10.1109/CDC.2013.6760004",

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note = "52nd IEEE Conference on Decision and Control, CDC 2013 ; Conference date: 10-12-2013 Through 13-12-2013",

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Seuret, A, Gouaisbaut, F & Fridman, E 2013, Stability of systems with fast-varying delay using improved Wirtinger's inequality. in 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013., 6760004, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 946-951, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 10/12/13. https://doi.org/10.1109/CDC.2013.6760004

Stability of systems with fast-varying delay using improved Wirtinger's inequality. / Seuret, Alexandre; Gouaisbaut, Frédéric; Fridman, Emilia.
2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 946-951 6760004 (Proceedings of the IEEE Conference on Decision and Control).

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

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AB - This paper considers the stability of systems with fast-varying delay. The novelty of the paper comes from the consideration of a new integral inequality which is proved to be less conservative than the celebrated Jensen's inequality. Based on this new inequality, a dedicated construction of Lyapunov-Krasovskii functionals is proposed and is showed to have a great potential in practice. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality, recently provided in the literature, in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

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Stability of systems with fast-varying delay using improved Wirtinger's inequality

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