State estimation for multi-layer complex dynamical networks with time delays

In this paper, we investigate the state estimation problem of multi-layer complex dynamical networks with coupling delays. Since the transmission of information will take time, which will affect the process of state estimation for multi-layer complex dynamical networks. First, we consider two kinds of delays in the network model: the intra-layer coupling delay and the inter-layer coupling delay. Then, an observer network with the same node dynamics and topological structure as the original multi-layer complex dynamical network is constructed and the error dynamical network can also be obtained. Lyapunov stability theory is used to solve the observer gain matrix and prove the asymptotic stability of the error dynamical network. Sufficient conditions for the state estimation are derived in the form of linear matrix inequalities. Finally, illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme.