On the output stabilizability of the diffusion equation
Faouzi Haddouchi
TL;DR
This paper investigates the conditions under which a one-dimensional diffusion equation's output can be stabilized, providing necessary and sufficient criteria based on eigenvalues and Fourier coefficients.
Contribution
It offers a complete characterization of output stabilizability for a simplified diffusion equation using spectral properties.
Findings
Conditions for output stabilizability are derived in terms of eigenvalues.
Necessary and sufficient criteria are established.
The results connect spectral properties with control design.
Abstract
This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be given. These conditions are given in terms of the eigenvalues of the infinitesimal generator and the Fourier coefficients of input and output operators.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Differential Equations and Numerical Methods · Advanced Mathematical Modeling in Engineering