On local ISS of nonlinear second-order time-delay systems without damping

Alexander Aleksandrov, Denis Efimov*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For a second-order system with vector position, either constant or time-varying delays, and a power nonlinearity of the degree higher than one, which does not contain a velocity-proportional damping term, the conditions of local input-to-state stability are proposed. The result is based on application of Lyapunov-Razumikhin approach, for which new time estimates on decay of solutions are obtained. The approach is extended to attitude stabilization of a rigid body, and it is illustrated by simulations.

Original languageEnglish
JournalInternational Journal of Robust and Nonlinear Control
StateAccepted/In press - 2024


FundersFunder number
Israel Science Foundation‐National Natural Science Foundation of China Joint Research Program3054/23
Ministry of Education and Science of the Russian Federation075‐15‐2021‐573
Israel Science Foundation673/19


    • input-to-state stability
    • Lyapunov-Razumikhin function
    • time-delay systems


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