Constrained H∞ control for the reaction-diffusion systems with spatiotemporal uncertainty

In this paper, an LMI-based H
∞
control is proposed for a class of reaction-diffusion systems subject to the actuator saturation and spatiotemporal uncertainty. Based on the Lyapunov’s direct method, a sufficient condition is initially derived to stabilize the original closed-loop system. Subsequently, the distributed and boundary-based H
∞
control is obtained in terms of linear matrix inequalities (LMIs) to give a tradeoff between actuator saturation and anti-disturbance performance. Then, a recursive algorithm is explicitly presented by combining the LMI optimization technology and spatial difference method. Finally, a comparison simulation study is performed to illustrate the effectiveness of proposed methodology.