The transient stabilization and voltage regulation problem for a synchronous generator connected to an infinite bus is addressed, in this technical note, in the presence of all uncertain physical parameters. First, new interpretations for the Desensitized Four Loops Regulator, here referred to as robust coordinated PSS-AVR (Power System Stabilizer & Automatic Voltage Regulator), are derived in terms of minimum phase properties with respect to a suitably chosen output for the linearized error system. Secondly, on the basis of such an output, a nonlinear generalization of the robust coordinated PSS-AVR is designed with the aim of enlarging the stability region and improving the transients about the unpredictable operating conditions determined by the faults. Its linear action coincides with the one provided by the robust coordinated PSS-AVR: the compelling simplicity of control structure (just one integrator is involved) and robust tuning procedure of the linear design are definitely inherited, with, additionally, no use of the mechanical input power. A numerical analysis along with realistic simulations confirm improved stability when the proposed nonlinear controller is applied.