This paper presents a novel application of multivariable frequency-domain control theory to the design of excitation-based stabilizers for large-scale electric power systems. The stabilizers are designed to coordinate the global performance of the multimachine system, and in some cases may turn out to be of a decentralized structure. The design procedure is based on the direct Nyquist array, supplemented by the characteristic function. The control design procedure is applied to a sample twelve-machine electrical power system which includes detailed models of synchronous machines, excitation systems, turbines, and speed governing mechanisms. Simulation results presented in this paper show that the design method leads to the removal of the underdamped oscillations, to a reduction in the interaction between the generating units, and to a significant improvement in the dynamical performance of the system. This is the first successful application of the direct Nyquist array method to the systematic design of excitation-based power system stabilizers for large-scale power systems.