An optimal reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Article Dans Une Revue Automatica Année : 2017

An optimal reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay

Résumé

This paper is concerned with stability of a linear system with a time-varying delay. First, an optimal reciprocally convex inequality is proposed. Compared with the extended reciprocally convex inequality recently reported, the optimal reciprocally convex inequality not only provides an optimal bound for the reciprocally convex combination, but also introduces less slack matrix variables. Second, a new Lyapunov-Krasovskii functional is tailored for the use of auxiliary function-based integral inequality. Third, based on the optimal reciprocally convex inequality and the new Lyapunov-Krasovskii functional, a stability criterion is derived for the system under study. Finally, two well-studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time-varying delay than some existing methods.
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Dates et versions

hal-01699185 , version 1 (16-05-2018)

Identifiants

Citer

Xian-Ming Zhang, Qing-Long Han, Alexandre Seuret, Frédéric Gouaisbaut. An optimal reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay. Automatica, 2017, 84, pp.221 - 226. ⟨10.1016/j.automatica.2017.04.048⟩. ⟨hal-01699185⟩
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