Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach

Abstract

This paper addresses the problem of robust $H_{\infty }$ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust $H_{\infty }$ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed $H_{\infty }$ performance of disturbance attenuation. Moreover, a suboptimal $H_{\infty }$ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.