Robust Boundary Output-Feedback Control of a Reaction-Diffusion Equation with In-Domain Disturbances

Francesco Ferrante (), Suha Shreim and Christophe Prieur ()
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Francesco Ferrante: University of Perugia
Suha Shreim: Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab
Christophe Prieur: Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 28, 32 pages

Abstract: Abstract Output feedback control design for a class of reaction-diffusion equations with Dirichlet anti-collocated sensing and actuation subject to in-domain disturbances is addressed. Within this setting, we design a finite-dimensional dynamic output feedback controller ensuring closed-loop exponential stability and input-output stability with an explicit estimate of the input-output gain. The approach is based on the spectral decomposition of the open-loop infinite-dimensional system and on the use of a suitable Lyapunov functional candidate. Sufficient conditions in the form of matrix inequalities are given to ensure closed-loop stability. These conditions are shown to be always feasible and are employed to devise an optimal controller design algorithm based on the solutions to some linear matrix inequalities.

Keywords: Partial differential equations; output feedback control; robust control; LMIs; Lyapunov methods (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02724-2

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