Exponential stabilization of infinite-dimensional systems by finite-dimensional controllers
Optimization and Control
2023-09-06 v1
Abstract
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The proof of closed-loop stability is based on a novel input-output gain introduced in this paper. For systems satisfying a property we call quasi-finite, an equivalent characterization of feedback stabilizability is obtained. Quasi-finiteness is verified for classes of parabolic and hyperbolic equations.
Cite
@article{arxiv.2309.01934,
title = {Exponential stabilization of infinite-dimensional systems by finite-dimensional controllers},
author = {Tian Xia and Giacomo Casadei and Francesco Ferrante and Luca Scardovi},
journal= {arXiv preprint arXiv:2309.01934},
year = {2023}
}