The state-vector approach is employed to describe discrete control systems with linear plants. A novel formulation is proposed to obtain “minimum-time” solution through the application of linear programming. For a given initial state, the systematic iterative process employed yields the minimum control time required and its corresponding controlling sequence to bring the system to its equilibrium state. The control input is magnitude-limited. This iterative process also reveals whether or not the controlling sequence is unique. When the controlling sequence of the minimum-time solution is not unique, two objective functions are suggested to continue the process, so that a choice can be made to satisfy the minimum fuel criterion. This iterative process is not restricted by the order of the plant. It can be easily executed on a digital computer. An illustrative example is worked out in detail in the paper.