Parameter-Dependent Feedback Compensator Design for a Space-Varying PDE and its Application in Steelmaking Processes

This paper presents a Lyapunov-based parameter-dependent feedback compensator design method for a linear reaction-diffusion equation subject to a space-varying reaction coefficient. In the proposed design method, the reaction coefficient is written in a parametric form under its boundedness assumption. By using the parametric form for the reaction coefficient and multiple collocated observation outputs, two types of parameter-dependent output feedback compensators: static output feedback and observer-based output feedback, are constructed such that the resulting closed-loop equation is exponentially stable. By applying the Lyapunov technique with variants of Poincaré-Wirtinger's inequality, sufficient conditions for the existence of these two types of feedback compensators are presented in terms of standard linear matrix inequalities. Finally, simulation results for the steelmaking processes are presented to support the proposed design method.