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Abstract and Applied Analysis
Volume 2014, Article ID 631071, 8 pages
Research Article

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

1School of Informatics, Linyi University, Linyi 276005, China
2School of Science, Linyi University, Linyi 276005, China
3School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received 25 September 2013; Accepted 5 November 2013; Published 12 January 2014

Academic Editor: Qiankun Song

Copyright © 2014 Cheng-Dong Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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