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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 418258, 7 pages
http://dx.doi.org/10.1155/2014/418258
Research Article

Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control

1School of Automation and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing 210096, China
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 16 December 2013; Revised 27 January 2014; Accepted 9 February 2014; Published 16 March 2014

Academic Editor: Wei Lin

Copyright © 2014 Kun Yuan 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.

Abstract

By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. First, based on Kronecker product and Lyapunov functional, some easy-to-test sufficient condition is given to ensure the synchronization of coupled DPS with time delay. Secondly, in the case that the whole coupled system cannot synchronize by itself, the proportional-spatial derivative (P-sD) state feedback controller is designed and applied to force the network to synchronize. The sufficient condition on the existence of synchronization controller is given in terms of a set of linear matrix inequalities. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.