This paper gives a norm bounding closed loop solution to a discrete, linear time-varying fixed finite horizon control problem. Methods of computing the achieved closed loop norms are considered. It is shown that the Riccati equation associated with the synthesis of the control is equivalent to the Riccati equation associated with a bounded real type result when invoked with the minimal closed loop dynamics. By showing a relationship between three time-varying Riccati equations, the optimum norm for the closed loop solution to the normalized left factor perturbed problem is explicitly obtained in terms of the Hankel norm of the normalized left factors. Explicit controller formulae are derived for a particular class of problem. A class of sub-optimal solutions, where the terminal state weighting matrix is non-zero, is considered. Solutions to a one degree-of-freedom intercept problem are compared for the cases when zero and non-zero terminal state weights are used.