State estimation for multi-layer complex dynamical networks with time-varying delay

This paper investigates the state estimation problem for a general kind of multi-layer complex dynamical networks with time-varying delay, which has not been studied yet. In this multi-layer complex dynamical network model, each layer has different number and dynamics of nodes, and the links between layers are arbitrary. First, we construct an observer network whose node dynamics and topological structure are the same as the original network. Second, we design the controller of the observer network and prove its effectiveness by the way of verifying the asymptotic stability of the error dynamics through Lyapunov stability theory. The gain matrices of the controller are obtained by solving linear matrix inequalities with Matlab. At last, a numerical simulation example is given to prove the correctness of the proposed scheme.