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Journal Articles IET Control Theory and Applications Year : 2019

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.

Domains

Automatic

Dates and versions

hal-01920425 , version 1 (13-11-2018)

Identifiers

Cite

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