A design procedure is proposed for synthesizing a linear-quadratic-Gaussian (LQG) optimal controller to obtain excess robustness optimization against noise spectral uncertainties, non-linear time-varying (NLTV) unmodelled dynamics in the discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodelled dynamics and constrained actuators. An algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favourable cost functional J but also to maximize the excess robustness with respect to H infinity-norm criterion by selecting two adequate weighting matrices Q(z) and R(z). We shall adopt the transfer function approach and two weighting matrices in the cost functional are shaped via the inverse LQG method to achieve excess robustness optimization.