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Pré-Publication, Document De Travail Année : 2024

On stability of nonlinear homogeneous systems with distributed delays having variable kernels

Alexander Aleksandrov
Emilia Fridman
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Résumé

The stability problem for nonlinear homogeneous systems with distributed delay and variable kernel is studied. Both, the Lyapunov-Krasovskii and the Razumikhin, approaches are applied. It is proved that the global asymptotic stability of the zero solution for an auxiliary delay-free homogeneous system implies the local asymptotic stability of the zero solution for the original system with distributed delay. Moreover, the impact of nonlinear time-varying perturbations on the system dynamics is analyzed applying the averaging techniques. The results are illustrated by a mechanical system described by a Lienard equation, and an indirect control system design for a linear system.

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Automatique
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Dates et versions

hal-04463938 , version 1 (17-02-2024)

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  • HAL Id : hal-04463938 , version 1

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Alexander Aleksandrov, Denis Efimov, Emilia Fridman. On stability of nonlinear homogeneous systems with distributed delays having variable kernels. 2024. ⟨hal-04463938⟩
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