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

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  • Cheng-Dong Yang
  • Jianlong Qiu
  • Jun-Wei Wang

Abstract

This paper addresses the problem of robust H∞ 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∞ P‐sD controller is developed such that the closed‐loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. Moreover, a suboptimal H∞ 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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:631071
DOI: 10.1155/2014/631071
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