In this paper, we study the control of the dynamic system governed by the matrix differential equation, x˙ = Fx + Du, x(0) = −c, where the input vector u is constrained in amplitude. It is shown that in the discrete (sampled data) case: (a) The general optimal control problem can be formulated as a nonlinear programming problem amenable to treatment by techniques developed in the operation research field. (b) The specific time optimal control problem originally studied by Kalman is treated here using a different approach which yields well-known as well as new results.