This paper studies a control design approach for certain linear discrete-time systems of single input and single output where an assumption of minimum phase systems and detecting correct delay-time are not required. First, we derive a condition for the optimum finite settling trajectory of the system. Then, we find that a control to transfer output and input value of the system to the optimum finite settling trajectories, which are successively predicted at every sampling time, is obtained in an output feedback form which is derived from the above condition. We verify that all control systems designed on the basis of the design method proposed in this paper are asymptotically stable without requiring any condition of systems to be controlled. This design method can be immediately extended to adaptive control by adding a suitable on-line model identifier. This adaptive control scheme is applicable to chemical plants which have uncertain and changing large time lags.