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arXiv · 2309.01934

Exponential stabilization of infinite-dimensional systems by finite-dimensional controllers

Tian Xia·Giacomo Casadei·Francesco Ferrante·Luca Scardovi
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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.

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Tian Xia, Giacomo Casadei, Francesco Ferrante, Luca Scardovi. 2023-09-05. Exponential stabilization of infinite-dimensional systems by finite-dimensional controllers. https://arxiv.org/abs/2309.01934

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