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Estimation of the necessary order of Legendre-LMI conditions to assess stability of time-delay systems

Abstract : This paper investigates the stability analysis of time-delay systems through Lyapunov arguments. Using the existence of a complete Lyapunov-Krasovskii functional and relying on polynomial approximation theory, our main goal is to approximate the complete Lyapunov functional and to take profit of a supergeometric convergence rate of the truncated error part. Necessary and sufficient conditions in the linear matrix inequality (LMI) framework for sufficiently large approximated orders are consequently proposed. Moreover, an estimation of the necessary order is provided analytically with respect to system parameters.
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https://hal.laas.fr/hal-03666571
Contributor : Mathieu Bajodek Connect in order to contact the contributor
Submitted on : Thursday, May 12, 2022 - 3:31:25 PM
Last modification on : Monday, July 4, 2022 - 9:44:35 AM

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  • HAL Id : hal-03666571, version 1

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Mathieu Bajodek, Alexandre Seuret, Frédéric Gouaisbaut. Estimation of the necessary order of Legendre-LMI conditions to assess stability of time-delay systems. 2022. ⟨hal-03666571⟩

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