A synthesis methodology is presented for designing time-dependent discrete-linear control systems such that the given performance specifications are satisfactorily met over a finite time horizon. A time-dependent discrete-linear optimal controller structure is employed and a standard mathematical programming algorithm is used to calculate the state weighting matrix Q and the final state weighting matrix P(f) so as to satisfy the performance specifications. To the knowledge of the authors the proposed design procedure for time-dependent deterministic plants is new. The application of the method is demonstrated in the control of two different time-varying plants.