TY - JOUR

T1 - On robust stability of delayed Lienard systems

AU - Александров, Александр Юрьевич

AU - Efimov, Denis V.

AU - Xubin, Ping

AU - Fridman, E.

PY - 2026/11/1

Y1 - 2026/11/1

N2 - The problem of robust stability is considered for mechanical systems described by Lienard differential equations with pointwise or distributed delays, where all nonlinearities are homogeneous functions of different degrees. To this end, qualitative stability conditions are derived for an auxiliary delay-free system, and next they are used to construct different Lyapunov–Krasovskii functionals for delayed counterparts. The influence of time-varying perturbations is investigated using the averaging theory. The focus is put on importance for robustness of a mild relation between the homogeneity degrees. The rates of convergence for the solutions are evaluated. The results are illustrated by simulations for an academic example.

AB - The problem of robust stability is considered for mechanical systems described by Lienard differential equations with pointwise or distributed delays, where all nonlinearities are homogeneous functions of different degrees. To this end, qualitative stability conditions are derived for an auxiliary delay-free system, and next they are used to construct different Lyapunov–Krasovskii functionals for delayed counterparts. The influence of time-varying perturbations is investigated using the averaging theory. The focus is put on importance for robustness of a mild relation between the homogeneity degrees. The rates of convergence for the solutions are evaluated. The results are illustrated by simulations for an academic example.

KW - Lienard systems

KW - Robust stability

KW - Time-delay systems

UR - https://www.mendeley.com/catalogue/25b02af2-51a9-3681-abbc-8418c2926bc2/

U2 - 10.1016/j.automatica.2026.113262

DO - 10.1016/j.automatica.2026.113262

M3 - Article

VL - 193

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 113262

ER -