Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques
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.
Keywords
Cite
@article{arxiv.1808.05370,
title = {Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques},
author = {Swann Marx and Yacine Chitour and Christophe Prieur},
journal= {arXiv preprint arXiv:1808.05370},
year = {2018}
}