Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers

作     者：XIANG LinYing LIU ZhongXin CHEN ZengQiang YUAN ZhuZhi 

作者机构：Department of Automation Nankai University Tianjin 300071 China 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2008年第51卷第5期

页      面：511-523页

核心收录：

学科分类：0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 071101[理学-系统理论] 0810[工学-信息与通信工程] 0711[理学-系统科学] 0802[工学-机械工程] 0835[工学-软件工程] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 080201[工学-机械制造及其自动化] 

基　　金：the National Natural Science Fundation of China (Grant Nos. 60774088 and 60574036) the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050055013) and the Program for New Century Excellent Talents of China (NCET) 

主　　题：complex dynamical network linear matrix inequality (LMI) weighted network pinning control hetero-geneous delay 

摘      要：Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities （LMIs）, which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogenous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.