Adaptive synchronization of complex dynamical networks with neural networks nodes and unmatched parameters

This letter is on the design problem of global asymptotical adaptive synchronization for a class of complex dynamical networks. In the considered networks, the dynamics of each node are approximated by a class of neural networks (NNs). The parameters of the NNs in the complex dynamical networks are unmatched with the ones in the desired dynamical system. Furthermore, the coefficient matrix of the adaptive controller under consideration is an arbitrary matrix instead of an identity one. An adaptive nonlinear controller is developed. By using Lyapunov method and some properties of Kronecker product, some sufficient conditions are proposed to ensure the dynamics of the considered network globally asymptotically synchronize with the desired solution. In particular, the proposed criteria for network synchronization are in terms of linear matrix inequalities. Only two variables are used in each criterion and the variables are not inside of any Kronecker product. Hence, the conditions are easy to check. A numerical example is presented to show the effectiveness and applicability of the proposed approach.