The problem of bounded-variance finite-time regulation of linear, discrete time-varying, uncertain systems with a norm bounded unknown parameter matrix is considered. An upper-bound on the value of the standard LQG control criterion is obtained for all the admissible systems. Regulators that minimize this bound are obtained, they consist of an optimal state-feedback gain and a robust state observer. Robust H-2-tracking problems are also treated where the output of the system should follow a reference sequence that is either perfectly known in advance, or previewed in a fixed-interval of time ahead.