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Input-to-State Stability of Homogeneous Infinite Dimensional Systems with Locally Lipschitz Nonlinearities

Andrey Polyakov 1
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 Input-to-State Stability (ISS) of homogeneous evolution equations in Banach spaces with unbounded linear operators and locally Lipschitz nonlinearities in the right-hand sides is studied. A new homogeneous converse Lyapunov theorem is presented. Similarly to finite-dimensional models, it is shown that the uniform asymptotic stability of an unperturbed homogeneous evolution equation implies its ISS with respect to homogeneously involved exogenous inputs.
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https://hal.inria.fr/hal-02541282
Contributor : Andrey Polyakov Connect in order to contact the contributor
Submitted on : Monday, February 15, 2021 - 11:24:24 AM
Last modification on : Friday, April 1, 2022 - 3:49:24 AM

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Andrey Polyakov. Input-to-State Stability of Homogeneous Infinite Dimensional Systems with Locally Lipschitz Nonlinearities. Automatica, Elsevier, 2021, ⟨10.1016/j.automatica.2021.109615⟩. ⟨hal-02541282v2⟩

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