Robust \(H_\infty\) control for a class of nonlinear distributed parameter systems via proportional-spatial derivative control approach
Summary: 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.
scientific article; zbMATH DE number 7022777