There is a large number of digital controls applied in permanent magnet synchronous generators (PMSG). There has been concern about the wide-band oscillation stability influenced by digital control delay in a power system including PMSG. To analyze the mechanism of wide-band oscillation instability deeply and assess system stability rapidly and accurately, both a new impedance modeling method and stability criterion are proposed. First, with the exact discretization method, a PMSG including digital control delay and system components in the receiving-end AC grid are modeled as z-domain impedance in the d-q frame generated by phase-locked loop (PLL). Subsequently, using electric circuit principles, all system components are aggregated into z-domain aggregation impedance. Secondly, based on the Gershgorin Theorem, a generalized forbidden region criterion is proposed to analyze system stability. Finally, a modified IEEE3-machine 9-bus system including PMSG model is built in Matlab/Simulink to verify the effectiveness of the proposed method.