TY - JOUR

T1 - On stability of nonlinear homogeneous systems with distributed delays having variable kernels

AU - Александров, Александр Юрьевич

AU - Efimov, Denis V.

AU - Fridman, Emilia

PY - 2024/8/1

Y1 - 2024/8/1

N2 - 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.

AB - 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.

KW - Averaging method

KW - Distributed delay

KW - Homogeneous systems

UR - https://www.sciencedirect.com/science/article/abs/pii/S0167691124001415?via%3Dihub

UR - https://www.mendeley.com/catalogue/1d4a77cc-20df-32af-9bc2-89b5259bc01d/

U2 - 10.1016/j.sysconle.2024.105853

DO - 10.1016/j.sysconle.2024.105853

M3 - Article

VL - 190

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

M1 - 105853

ER -