Spatial-Differential Linear Matrix Inequality-based Distributed H∞ Control for the Coupled Parabolic PDEs System

This paper investigates the distributed H ∞ control for a class of semi-linear systems, which are modeled by the coupled parabolic partial differential equations (PDEs) with the input saturation. To stabilize the system, we derive a sufficient condition based on the Lyapunov-Krasovskii candidate function. Namely, the existence of H ∞ controller is transformed as the spatial differential linear matrix inequality (LMI) to obtain the distributed gains of spatial domain. With the finite difference discretization method, the numerical solution of closed-loop system demonstrates the effectiveness of proposed controller.