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

Alexander Aleksandrov, Denis Efimov*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number111058
StatePublished - Jul 2023


Dive into the research topics of 'Stability of homogeneous systems with distributed delay and time-varying perturbations'. Together they form a unique fingerprint.

Cite this