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Conference Papers Year : 2023

Analysis of homogeneous systems with distributed delay using averaging approach

Alexander Aleksandrov
Emilia Fridman
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Abstract

The conditions for stability of the zero solution are formulated for homogeneous dynamical systems of non-zero degree with distributed delays. It is assumed that if the disturbances are absent and the non-delayed state substitutes the delayed one, then the obtained nominal system is globally asymptotically stable. In such a case it is proven that in the disturbance-free scenario the zero solution is locally asymptotically stable for positive degree and practically globally asymptotically stable for negative degree. Using averaging tools, the influence of time-varying disturbances is investigated and the respective stability margins are derived. Finally, the obtained theoretical findings are illustrated by a mechanical example.
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hal-04176143 , version 1 (02-08-2023)

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  • HAL Id : hal-04176143 , version 1

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Alexander Aleksandrov, Denis Efimov, Emilia Fridman. Analysis of homogeneous systems with distributed delay using averaging approach. IFAC 2023 - 22nd IFAC World Congress, Jul 2023, Yokohama, Japan. ⟨hal-04176143⟩
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