On converse Lyapunov theorem for fixed-time input-to-state stability - Contrôle et estimation en temps fini pour les systèmes distribués Access content directly
Journal Articles SIAM Journal on Control and Optimization Year : 2023

On converse Lyapunov theorem for fixed-time input-to-state stability

Abstract

Input-to-state stability is one of the most utilizable robust stability properties for nonlinear dynamical systems, while (nearly) fixed-time convergence is a kind of decay for trajectories of disturbance-free systems that is independent in initial conditions. The presence of both these features for a system can be checked by existence of a proper Lyapunov function. The objective of this work is to provide the conditions for a converse result that (nearly) fixed-time input-to-state stable systems admit a respective Lyapunov function. Similar auxiliary results for uniform finite-time stability and uniform (nearly) fixed-time stability are obtained.
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hal-04274297 , version 1 (15-11-2023)

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  • HAL Id : hal-04274297 , version 1

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Denis Efimov, Andrey Polyakov. On converse Lyapunov theorem for fixed-time input-to-state stability. SIAM Journal on Control and Optimization, inPress. ⟨hal-04274297⟩
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