On stability of nonlinear homogeneous systems with distributed delays having variable kernels
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.
Domaines
Automatique
Origine : Fichiers produits par l'(les) auteur(s)