A minimum-time control problem of a linear system is reduced to a problem of L.P. (Linear Programming), when it is considered in the sampled-mode control. In this case, if we take the sampling-interval small, then a solution, which is given by this sampled-mode system, will be available as the first approximation of a solution of the continuous system. Therefore, by reducing the sampled-mode control to Bang-Bang type control and evaluating the variation of the terminal time point by variations of switching-times, this continuous-type problem can be solved by L.P. too. Then an accuracy which is given by this method is within the error of the order of 10-4 in term of a norm of χ, ||χ||. This accuracy is acceptable, compared with Yamaguchi's, Plants's and others.
In one word, this report describes a method which solves a minimum-time control problem of a linear system by L.P., which is a usual and simple procedure.