This paper presents an innovative stability analysis and design approach for time-domain impedance boundary conditions to simulate noise propagation and radiation from a lined turbomachinery duct in the presence of a mean flow. A control-oriented model is developed for the stability analysis of the impedance boundary condition by using generalized function at the lining surface. The mean flow effect and sound propagation are considered in the model as well. Then, the numerical stability issue is analyzed by using the Bode plots before stabilized accordingly by employing the phase lead compensator method, which results in a rational transfer function. Finally, the corresponding time-domain implementation is achieved by using the so-called controllable canonical form rather than an inconvenient convolution operation. The performance of the current proposed approach is first validated in an in-duct propagation case by comparing to analytical solutions obtained by employing the WienerβHopf method and then demonstrated in a couple of duct acoustic problems with representative turbomachinery setups. The innovative cross-disciplinary nature of the current proposed approach can shed light on impedance problems and is very useful to time-domain acoustic simulations for turbomachinery applications.