TY - JOUR

T1 - Polystability Conditions for Some Classes of Nonlinear Time-Delay Systems

AU - Александров, Александр Юрьевич

PY - 2025/4/8

Y1 - 2025/4/8

N2 - The paper addresses to the stability analysis of some classes of nonlinear time-delay systems. Both cases of constant and cases of distributed delays are studied. Using the Lyapunov direct method, sufficient conditions of polystability by nonlinear homogeneous approximation are derived. In addition, the obtained results are extended to the scenario where a system of the first approximation is linear with respect to one part of state variables and nonlinear homogeneous with respect to another one. Some examples of applications of the proposed approaches to the stability analysis of mechanical systems are provided.

AB - The paper addresses to the stability analysis of some classes of nonlinear time-delay systems. Both cases of constant and cases of distributed delays are studied. Using the Lyapunov direct method, sufficient conditions of polystability by nonlinear homogeneous approximation are derived. In addition, the obtained results are extended to the scenario where a system of the first approximation is linear with respect to one part of state variables and nonlinear homogeneous with respect to another one. Some examples of applications of the proposed approaches to the stability analysis of mechanical systems are provided.

KW - Lyapunov-Krasovskii functional

KW - delay

KW - differential inequality

KW - nonlinear systems

KW - partial stability

KW - polystability

UR - https://epubs.siam.org/doi/full/10.1137/24M1676971

UR - https://www.mendeley.com/catalogue/0eb60ee4-4666-304f-a530-c4a45a482aa2/

U2 - 10.1137/24m1676971

DO - 10.1137/24m1676971

M3 - Article

VL - 63

SP - 1085

EP - 1103

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 2

ER -