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Converse Lyapunov-Krasovskii theorem for ISS of neutral systems in Sobolev spaces

Denis Efimov 1 Emilia Fridman 2
1 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : The conditions of existence of a Lyapunov-Krasovskii functional (LKF) for nonlinear input-to-state stable (ISS) neutral type systems are proposed. The system under consideration depends nonlinearly on the delayed state and the delayed state derivative, and satisfies the conditions for the existence and uniqueness of the solutions. The LKF and the system properties are defined in a Sobolev space of absolutely continuous functions with bounded derivatives.
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Denis Efimov, Emilia Fridman. Converse Lyapunov-Krasovskii theorem for ISS of neutral systems in Sobolev spaces. Automatica, Elsevier, 2020, 118, ⟨10.1016/j.automatica.2020.109042⟩. ⟨hal-02554143⟩

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