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Journal Articles Automatica Year : 2023

Stability of homogeneous systems with distributed delay and time-varying perturbations

Abstract

For a class of nonlinear systems with homogeneous right-hand sides of non-zero degree and distributed delays, the problem of stability robustness of the zero solution with respect to time-varying perturbations multiplied by a nonlinear functional gain is studied. It is assumed that the disturbance-free and delay-free system (that results after substitution of non-delayed state for the delayed one) is globally asymptotically stable. First, it is demonstrated that in the disturbance-free case the zero solution is either locally asymptotically stable or practically globally asymptotically stable, depending on the homogeneity degree of the delay-free counterpart. Second, using averaging tools several variants of the time-varying perturbations are considered and the respective conditions are derived evaluating the stability margins in the system. The results are obtained by a careful choice and comparison of Lyapunov-Krasovskii and Lyapunov-Razumikhin approaches. Finally, the obtained theoretical findings are illustrated on two mechanical systems.

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Automatic
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Dates and versions

hal-03777752 , version 1 (15-09-2022)
hal-03777752 , version 2 (12-01-2024)

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Alexander Aleksandrov, Denis Efimov, Emilia Fridman. Stability of homogeneous systems with distributed delay and time-varying perturbations. Automatica, 2023, 153, pp.111058. ⟨10.1016/j.automatica.2023.111058⟩. ⟨hal-03777752v2⟩
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