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

2023/09/05 by Xia, Tian, Casadei, Giacomo, Ferrante, Francesco +1
#93C20 #93D15 #93D25 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2309.01934

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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