Abstract: The paper studies the problem of robust LQG state-feedback control with H∞ performance bound for uncertain linear discrete-time systems that are subjected to norm-bounded parameter uncertainty. Both the cases of finite horizon time-varying and infinite horizon time-invariant are considered. The controller derived can satisfy a given H∞ performance bound and provide an optimized bound for the worst-case H∞ performance index for all admissible parameter uncertainties, and also make the closed-loop systems asymptotically stable for the case of infinite horizon time-invariant. The obtained result only needs to solve a single parameter dependent Riccati equation.