Stability of homogeneous systems with ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Stability of homogeneous systems with distributed delay and time-varying perturbations
Author(s) :
Aleksandrov, Alexander [Auteur]
Saint Petersburg University [SPBU]
Efimov, Denis [Auteur]
Finite-time control and estimation for distributed systems [VALSE]
Fridman, Emilia [Auteur]
Tel Aviv University [TAU]
Saint Petersburg University [SPBU]
Efimov, Denis [Auteur]

Finite-time control and estimation for distributed systems [VALSE]
Fridman, Emilia [Auteur]
Tel Aviv University [TAU]
Journal title :
Automatica
Pages :
111058
Publisher :
Elsevier
Publication date :
2023-07
ISSN :
0005-1098
HAL domain(s) :
Sciences de l'ingénieur [physics]/Automatique / Robotique
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
Comment :
Submitted to Automatica
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