Pinning control of complex dynamical networks with heterogeneous delays

Authors:
Linying Xiang;Zengqiang Chen;Zhongxin Liu;Fei Chen;Zhuzhi Yuan
Affiliations:
Department of Automation, Nankai University, Tianjin 300071, PR China;Department of Automation, Nankai University, Tianjin 300071, PR China;Department of Automation, Nankai University, Tianjin 300071, PR China;Department of Automation, Nankai University, Tianjin 300071, PR China;Department of Automation, Nankai University, Tianjin 300071, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

Complex dynamical networks with heterogeneous delays in both continuous- and discrete-time domains are controlled by applying local feedback injections to a small fraction of nodes in the whole network. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities (LMI), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to its equilibrium. In some particular cases, a single controller can achieve the control objective. Numerical simulations of various representative networks, including a globally coupled network, a star-coupled network and an Extended Barabasi-Albert (EBA) scale-free network, are finally given for illustration and verification.