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An overview of recent advances in stability of linear systems with time-varying delays

Abstract : This paper provides an overview and in-depth analysis of rec ent advances in stability of linear systems with time-varyi ng delays. First, recent developments of a delay convex analys is approach, a reciprocally convex approach and the constru ction of Lyapunov-Krasovskii functionals are reviewed insightful ly. Second, in-depth analysis of the Bessel-Legendre inequ ality and some affine integral inequalities is made, and recent stability r esults are also summarized, including stability criteria f or three cases of a time-varying delay, where information on the bounds of the t ime-varying delay and its derivative is totally known, part ly known and completely unknown, respectively. Third, a number of stabi lity criteria are developed for the above three cases of the t ime-varying delay by employing canonical Bessel-Legendre inequalitie s, together with augmented Lyapunov-Krasovskii functiona ls. It is shown through numerical examples that these stability criteria o utperform some existing results. Finally, several challen ging issues are pointed out to direct the near future research.
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Contributor : Alexandre Seuret Connect in order to contact the contributor
Submitted on : Tuesday, November 13, 2018 - 11:30:38 AM
Last modification on : Monday, July 4, 2022 - 9:46:40 AM

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Qing-Long Han, Xian-Ming Zhang, Alexandre Seuret, Frédéric Gouaisbaut, Yong He. An overview of recent advances in stability of linear systems with time-varying delays. IET Control Theory and Applications, Institution of Engineering and Technology, 2019, 13 (1), 15p. ⟨10.1049/iet-cta.2018.5188⟩. ⟨hal-01920425⟩



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