Comments on "Exact control of linear systems with multiple control"

This note is concerned with piecewise constant controls. In order to supplement the above-mentioned paper sufficient conditions for the existence of a piecewise constant control are provided. Moreover, although for an
n
-dimensional control system the switching times for the piecewise constant control cannot he chosen arbitrarily, it is shown that the switching times can be chosen as close as we wish to any preassigned collection of
n
time points. The proof of the main result is constructive and it provides an algorithm for the design of a piecewise constant control.