Output feedback stabilization of a reaction-diffusion PDE in the presence of saturations of the input and its time derivatives

Hugo Lhachemi (1) , Christophe Prieur (2)

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

This chapter tackles the output feedback stabilization of a reaction-diffusion PDE in the presence of saturations applying to the command input as well as a finite number of its time derivatives. The control strategy consists of a finite dimensional observer and a finite-dimensional state-feedback. We derive LMI-based sufficient conditions that ensure the local exponential stability of the closed-loop system while providing an estimation of the domain of attraction. These LMI conditions are shown to be feasible provided the order of the observer is selected large enough. The stability analysis is performed by using Lyapunov's direct method while invoking sector conditions commonly used for the analysis of saturated finite-dimensional systems.

Domaines: Automatique / Robotique

Hugo Lhachemi, Christophe Prieur. Output feedback stabilization of a reaction-diffusion PDE in the presence of saturations of the input and its time derivatives. Jean Auriol; Joachim Deutscher; Guilherme Mazanti; Giorgio Valmorbida. Advances in Distributed Parameter Systems, 14, Springer International Publishing, pp.45-68, 2022, Advances in Delays and Dynamics, 978-3-030-94765-1. ⟨10.1007/978-3-030-94766-8_3⟩. ⟨hal-03665183⟩