The discrete-time iterative map of digitally controlled DC-AC H-bridge inverter with outer load-voltage loop and inter inductance-current loop plus voltage-reference feedforward loop is derived by considering the effect of the time delay problems inherent in digital control system. The type of the bifurcation point when the system loses stability is predicted in terms of the eigenvalues of the Jacobian matrix,and it is found that the type is of the Hopf bifurcation. The analytic expressions of the stability boundaries and the oscillation frequency are deduced, and the underlying mechanism of this nonlinear phenomenon is analyzed. Finally, the theoretical results are verified by simulations and circuit experiments.