Based on the centre of inertia（COI） data provided by wide-area measurement system（WAMS） in power systems， a completely decoupled generator model can be constructed within COI-reference coordinate frame. According to Lyapunov theory and back-stepping concept， a simple and practical method is proposed for decentralized nonlinear excitation control design. This method is theoretically simple and all the three control parameters are very easy to determine. Moreover， there are only three control signals that should be sent to generators by WAMS. This considerably reduces the possibility of signal channel congestion. Simulation results on New England test power system（NETPS） show that this nonlinear excitation controller is robust to generator parameters， operating conditions and load types， meanwhile it allows the existence of time delays in COI signals and the permitted time delay covers almost all the types and all the ranges of time delays in WAMS data under normal system conditions.