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

Swann Marx 1 Yacine Chitour 2 Christophe Prieur 3
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
3 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
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 asymptotically stable with a linear damping. To do so, we use the fact that, for any linear infinite-dimensional system that is globally exponentially stable, there exists a Lyapunov functional. 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 which compensates the nonlinearity. Our results are then applied to the linearized Korteweg-de Vries equation and some wave equations.
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Submitted on : Friday, October 2, 2020 - 5:44:12 PM
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Swann Marx, Yacine Chitour, Christophe Prieur. Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2020, 65 (5), pp.2139-2146. ⟨10.1109/TAC.2019.2937495⟩. ⟨hal-02956449⟩

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