Abstract: To the problem of a class of interconnected large-scale power systems，which has characteristics of nonlinear interconnection function and variable time-delay，the design method of decentralized feedback controller is presented．First，the nonlinear function is converted into quadratically bounded inequalities in the subsystem state．Then based on Lyapunov stability theory，the matrix Schur complement formula and linear matrix inequalities ( LMIs) ，the delay-independent sufficient condition for asymptotic stability of power systems is given by constructing Lyapunov function．What’s more，the sufficient condition for constant time-delay is given as a special case．In addition，the simulation of a two-machine infinite bus power system has been done here．The simulation results of this power system show that the proposed method is feasible and valid．