An alternative stability analysis theorem for nonlinear periodic discrete-time systems is presented. The developed theorem offers a trade-off between conservatism and complexity of the corresponding stability test. In addition, it yields a tractable stabilizing controller synthesis method for linear periodic discrete-time systems subject to polytopic state and input constraints. It is proven that in this setting, the proposed synthesis method is strictly less conservative than available tractable synthesis methods. The application of the derived method to the satellite attitude control problem results in a large region of attraction.