Local output feedback stabilization of a Reaction-Diffusion equation with saturated actuation Article - Janvier 2023

Hugo Lhachemi, Christophe Prieur

Hugo Lhachemi, Christophe Prieur, « Local output feedback stabilization of a Reaction-Diffusion equation with saturated actuation  », IEEE Transactions on Automatic Control, janvier 2023, pp. 564 - 571. ISSN 0018-9286. 〈https://ieeexplore.ieee.org/document/9690038〉

Abstract

This paper is concerned with the output feedback stabilization of a reaction-diffusion equation by means of bounded control inputs in the presence of saturations. Using a finite-dimensional controller composed of an observer coupled with a finite-dimensional state-feedback, we derive a set of conditions ensuring the stability of the closed-loop plant while estimating the associated domain of attraction in the presence of saturations. This set of conditions is shown to be always feasible for an order of the observer selected large enough. The stability analysis relies on Lyapunov functionals along with a generalized sector condition classically used to study the stability of linear finite-dimensional plants in the presence of saturations.

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