A simple technique is introduced to synthesize an optimal controller, not only to minimize the least favourable cost functional J, but also to achieve the following purposes in discrete-time linear-quadratic-gaussian (LQG) optimal systems: (I) input-output decoupling; (2) stability robustness in the presence of non-linear time-varying (NLTV) unmodelled dynamics; (3) complete and arbitrary stable pole-placement; and (4) some zero-assignment, The Wiener-Hopí technique is employed and two weighting matrices Q(z) and R(z) of the quadratic cost functional are specified (by the inverse optimal control method), so that the controller is optimal with respect to the chosen weighting matrices and the design goals are achieved.