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Extensions of Razumikhin's Theorem and Lyapunov-Krasovskii Functional Constructions for Time-Varying Systems with Delay *

Abstract : We prove extensions of Razumikhin's theorem for time-varying continuous and discrete time nonlinear systems. Our results include a novel 'strictification' technique for converting a nonstrict Lyapunov function into a strict one. We also provide new constructions of Lyapunov-Krasovskii functionals that can be used to prove robustness to perturbations. Our examples include a key model from identification theory, and they show how our method can sometimes allow broader classes of delays than the results in the literature.
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https://hal.inria.fr/hal-01660097
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Submitted on : Saturday, December 9, 2017 - 11:32:49 PM
Last modification on : Wednesday, April 8, 2020 - 3:21:30 PM

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Frédéric Mazenc, Michael Malisoff. Extensions of Razumikhin's Theorem and Lyapunov-Krasovskii Functional Constructions for Time-Varying Systems with Delay *. Automatica, Elsevier, 2017, 78, pp.1-13. ⟨10.1016/j.automatica.2016.12.005⟩. ⟨hal-01660097⟩

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