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Journal Articles Automatica Year : 2021

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

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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Dates and versions

hal-02541282 , version 1 (13-04-2020)
hal-02541282 , version 2 (15-02-2021)

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