Polynomial Convergence of an Observer for an Infinite-Dimensional Oscillating System

This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear operators and explicitly construct the resolvent of the correspondi...

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Bibliographic Details
Main Authors Zuyev, Alexander, Kalosha, Julia
Format Journal Article
LanguageEnglish
Published 01.10.2024
Subjects
Mathematics - Optimization and Control
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Summary:This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear operators and explicitly construct the resolvent of the corresponding infinitesimal generator. The asymptotic behavior of the resolvent on the imaginary axis is studied to describe the rate of decay of the observation error. The estimated decay rate is illustrated through an example of an oscillating flexible structure with one-dimensional output.
DOI:10.48550/arxiv.2410.00989