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Lyapunov-Krasovskii characterization of the input-to-state stability for switching retarded systems

Abstract : In this paper we characterize various stability notions of nonlinear switching retarded systems by the existence of a common Lyapunov-Krasovskii functional with suitable conditions. We consider a general class of Lebesgue measurable switching signals. We provide an equivalence property showing that uniform input-to-state stability can be equivalently studied through the class of piecewise-constant inputs and piecewise-constant switching signals. Thanks to this equivalence property, we rely on what it is developed in the literature to provide direct and converse theorems for uniform input-to-state, asymptotic and exponential stability. Based on these results, we give a first order approximation theorem for nonlinear switching retarded systems. A link between the exponential stability of an unforced switching retarded system and the input-to-state stability property, in the case of measurable switching signals, is obtained. Examples showing the applicability of our results are also given.
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https://hal.archives-ouvertes.fr/hal-03233502
Contributor : Ihab Haidar <>
Submitted on : Monday, May 24, 2021 - 8:48:27 PM
Last modification on : Wednesday, July 21, 2021 - 2:16:02 PM

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  • HAL Id : hal-03233502, version 1

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Ihab Haidar, Pierdomenico Pepe. Lyapunov-Krasovskii characterization of the input-to-state stability for switching retarded systems. 2021. ⟨hal-03233502⟩

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