Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE
Abstract
This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a situation may arise, for instance, when the actuator admits a dynamics. The open-loop ODE is exponentially stable and the open-loop infinite-dimensional system is dissipative, i.e., the energy is nonincreasing, but its equilibrium point is not necessarily attractive. The feedback design is based on an extension of a finite-dimensional method, namely the forwarding method. We propose some sufficient conditions that imply the well-posedness and the global asymptotic stability of the closed-loop system. As illustration, we apply these results to a transport equation coupled with an ODE.
Keywords
Cite
@article{arxiv.2009.10379,
title = {Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE},
author = {Swann Marx and Lucas Brivadis and Daniele Astolfi},
journal= {arXiv preprint arXiv:2009.10379},
year = {2021}
}