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

Aleksandrov, A.Yu.; Efimov, Denis; Fridman, Emilia

Document type :

Pré-publication ou Document de travail

Title :

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

Author(s) :

Aleksandrov, A.Yu. [Auteur]
Saint Petersburg State University [SPBU]
Efimov, Denis [Auteur]

Finite-time control and estimation for distributed systems [VALSE]
Fridman, Emilia [Auteur]

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 >

Language :

Anglais

Comment :

Submitted to Automatica

Collections :