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Conference Papers Year : 2021

Stability Analysis using New Variant of Halanay's Inequality

Abstract

We present a generalized form of Halanay's inequality, having a time varying gain multiplying the delayed term and a constant decay rate. Unlike the usual Halanay's conditions where the decay rate is required to exceed an upper bound on the gain multiplying the delayed term, we provide less restrictive conditions that allow times when the decay rate can be strictly less than the gain. We include an application to continuous time systems with switched delay values. This illustrates the utility of our generalized Halanay's inequality conditions for proving asymptotic stability in significant cases that violate the contraction condition that was needed to prove asymptotic stability in previous trajectory based results, and which are also not amenable to previous Lyapunov function constructions.
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Dates and versions

hal-03431280 , version 1 (16-11-2021)

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Frederic Mazenc, Michael Malisoff, Miroslav Krstic. Stability Analysis using New Variant of Halanay's Inequality. MTNS 2021 -24th International Symposium on Mathematical Theory of Networks and Systems, Aug 2021, Cambridge, United Kingdom. ⟨10.1016/j.ifacol.2021.06.139⟩. ⟨hal-03431280⟩
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