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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2020

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

Swann Marx
Yacine Chitour

Résumé

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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Dates et versions

hal-02956449 , version 1 (02-10-2020)

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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, 2020, 65 (5), pp.2139-2146. ⟨10.1109/TAC.2019.2937495⟩. ⟨hal-02956449⟩
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