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

Author

Listed:
  • Kun Yuan
  • Abdulaziz Alofi
  • Jinde Cao
  • Abdullah Al-Mazrooei
  • Ahmed Elaiw

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.

Suggested Citation

  • Kun Yuan & Abdulaziz Alofi & Jinde Cao & Abdullah Al-Mazrooei & Ahmed Elaiw, 2014. "Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnddns:418258
    DOI: 10.1155/2014/418258
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