Pinning control of complex dynamical networks with heterogeneous delays

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 Barabási–Albert (EBA) scale-free network, are finally given for illustration and verification.