Pinning Control of the Coupled Distributed Parameter System with Time Delay

2018 ◽  
Vol 21 (3) ◽  
pp. 1250-1259 ◽  
Author(s):  
Kun Yuan ◽  
Kaifeng Zhang ◽  
Jinde Cao
Keyword(s):  
Time Delay ◽  
Pinning Control ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
System With Time Delay

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

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Kun Yuan ◽  
Abdulaziz Alofi ◽  
Jinde Cao ◽  
Abdullah Al-Mazrooei ◽  
Ahmed Elaiw
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Coupled System ◽  
Parabolic Partial Differential Equation ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Sufficient Condition ◽  
Spatial Derivative ◽  
Parameter System ◽  
System With Time Delay

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.

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