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

被引：5

作者：

Yuan, Kun ^{[1
,2
]}

Alofi, Abdulaziz ^{[3
]}

Cao, Jinde ^{[1
,2
,3
]}

Al-Mazrooei, Abdullah ^{[3
]}

Elaiw, Ahmed ^{[3
]}

机构：

[1] Southeast Univ, Minist Educ, Sch Automat, Nanjing 210096, Jiangsu, Peoples R China

[2] Southeast Univ, Minist Educ, Key Lab Measurement & Control Complex Syst Engn, Nanjing 210096, Jiangsu, Peoples R China

[3] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2014年 / 2014卷

关键词：

FINITE-DIMENSIONAL APPROXIMATION; FEEDBACK-CONTROL; CONTROL DESIGN; PDE SYSTEMS; OSCILLATORS; MODEL;

D O I：

10.1155/2014/418258

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：7

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