Stabilization of Delayed Networks with Different Nodes  

作　　者：徐君群 唐万生 张建雄 

机构地区：[1]Institute of Systems Engineering,Tianjin University

出　　处：《Transactions of Tianjin University》2011年第2期151-156,共6页天津大学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (No.61004015);Research Fund for the Doctoral Program of Higher Education of China (No.20090032120034)

摘　　要：In this paper,the control of complex delayed networks with different nodes is proposed.Firstly,the stabilization of coupled networks with time delay is investigated.By constructing a Lyapunov function,a linear feedback controller design procedure for the networks is converted to the problem of solving a set of linear matrix inequalities.Then the results are extended to networks with both delayed dynamical nodes and delayed couplings.It is shown that the stabilization of complex networks is determined by the dynamics of each uncoupled node,coupling matrix and feedback gain matrix of networks.Two examples are simulated.In the first example,a network with 10 nodes consisting of Lorenz systems and systems proposed by Zhang in 2009 is given.It is found that the network states are divergent without control,and convergent under designed linear feedback controllers.In the second example,a larger network with 100 nodes consisting of delayed Chen systems and delayed Lorenz systems is given.The proposed method is also effective for large scale networks.In this paper, the control of complex delayed networks with different nodes is proposed. Firstly, the stabilization of coupled networks with time delay is investigated. By constructing a Lyapunov function, a linear feedback controller design procedure for the networks is converted to the problem of solving a set of linear matrix inequalities. Then the results are extended to networks with both delayed dynamical nodes and delayed couplings. It is shown that the stabilization of complex networks is determined by the dynamics of each uncoupled node, coupling matrix and feedback gain matrix of networks. Two examples are simulated. In the first example, a network with 10 nodes consisting of Lorenz systems and systems proposed by Zhang in 2009 is given. It is found that the network states are divergent without control, and convergent under designed linear feedback controllers. In the second example, a larger network with 100 nodes consisting of delayed Chen systems and delayed Lorenz systems is given. The proposed method is also effective for large scale networks.

关 键 词：complex network time delay linear feedback linear matrix inequalities 

分 类 号：O157.5[理学—数学]