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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Francesco Ferrante & Suha Shreim & Christophe Prieur, 2025. "Robust Boundary Output-Feedback Control of a Reaction-Diffusion Equation with In-Domain Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-32, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02724-2
    DOI: 10.1007/s10957-025-02724-2
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