Anti-Windup Design for a Reaction-Diffusion Equation

This paper focuses on the anti-windup design for saturated 1-D linear reaction-diffusion equation which admits a finite number of unstable poles. We consider scenario in system is controlled via dynamic, finite-dimensional output feedback controller ensuring closed-loop exponential stability. A method proposed to dynamic compensator maximize region attraction and minimize effect external perturbations. More precisely, sufficient conditions local stability are derived expressed terms set matrix inequalities. Using generalized sector proper change variables, then recast as an optimization problem solving numerical example provided showcase highlight its effectiveness.