Finite-Time and Fixed-Time Input-to-State Stability: Explicit and Implicit Approaches

Francisco Lopez-Ramirez (1) , Denis Efimov (1) , Andrey Polyakov (1) , Wilfrid Perruquetti (2)

1 VALSE - Finite-time control and estimation for distributed systems
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

The present article gathers the analysis of non-asymptotic convergence rates (finite-time and fixed-time) with the property of input-to-state stability. Theoretical tools to determine this joint property are presented for the case where an explicit ISS Lyapunov function is known, and when it remains in implicit form (e.g. as a solution of an algebraic equation). For the case of finite-time input-to-state stability, necessary and sufficient conditions are given whereas for the fixed-time case only a sufficient condition is obtained. Academic examples and numerical simulations support the obtained results.

Mots clés: Finite-Time Stability; Fixed-Time Stability; Input-to-State Stability

Domaines: Automatique / Robotique

Francisco Lopez-Ramirez, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti. Finite-Time and Fixed-Time Input-to-State Stability: Explicit and Implicit Approaches. Systems and Control Letters, 2020, 144, ⟨10.1016/j.sysconle.2020.104775⟩. ⟨hal-02921837⟩