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Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques

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Abstract

In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is globally asymp-totically stable with a linear damping. To do so, we first characterize, in terms of Lyapunov functionals, several types of asymptotic stability for linear infinite-dimensional systems, namely the exponential and the polynomial stability. Then, we derive a Lyapunov functional for the nonlinear system, which is the sum of a Lyapunov functional coming from the linear system and another term with compensates the nonlinearity. Our results are then applied to the linearized Korteweg-de Vries equation and some wave equations.
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Dates and versions

hal-01857265 , version 1 (14-08-2018)
hal-01857265 , version 2 (14-09-2018)
hal-01857265 , version 3 (29-10-2018)
hal-01857265 , version 4 (04-12-2018)

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Swann Marx, Yacine Chitour, Christophe Prieur. Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques. European Control Conference (ECC 2018), Jun 2018, Limassol, Cyprus. ⟨hal-01857265v2⟩
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