Global Output Feedback Stabilization of Semilinear Reaction-Diffusion PDEs

Hugo Lhachemi (1, 2) , Christophe Prieur (3)

1 L2S - Laboratoire des signaux et systèmes
2 CentraleSupélec
3 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics

This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations, namely: bounded control operator and right Robin boundary control. The measurement is selected as a left Dirichlet trace. The control strategy is finite dimensional and is designed based on a linear version of the plant. We derive a set of sufficient conditions ensuring the global exponential stabilization of the semilinear reaction-diffusion PDE. These conditions are shown to be feasible provided the order of the controller is large enough and the size of the sector condition in which the semilinearity is confined into is small enough.

Mots clés: Semilinear reaction-diffusion PDEs; output feedback stabilization; finite-dimensional control

Domaines: Sciences de l'ingénieur [physics]

Hugo Lhachemi, Christophe Prieur. Global Output Feedback Stabilization of Semilinear Reaction-Diffusion PDEs. CPDE - 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, Sep 2022, Kiel, Germany. pp.53-58, ⟨10.1016/j.ifacol.2022.10.376⟩. ⟨hal-04159840⟩