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Mathematical Problems in Engineering
Volume 2015, Article ID 380903, 12 pages
Research Article

Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

1School of Informatics, Linyi University, Linyi 276005, China
2Provincial Key Laboratory for Network Based Intelligent Computing, Jinan 250022, China
3School of Science, Linyi University, Linyi 276005, China
4Department of Electrical and Computer Engineering, University of Rhode Island, Kingston, RI 02881, USA
5Science and Technology on Underwater Acoustic Antagonizing Laboratory, Systems Engineering Research Institute of CSSC, Beijing 100036, China
6School of Automobile Engineering, Linyi University, Linyi 276005, China
7School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Received 16 October 2014; Revised 12 April 2015; Accepted 15 April 2015

Academic Editor: Anna Vila

Copyright © 2015 Chengdong 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 exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.