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

Given a linear system , where and are and matrices, with and is of full rank, Farlow\´s theorem in the paper gives a necessary condition for the existence of coefficients for rectangular pulse functions that constitute the control vector, so that the state of the system is driven to zero in a finite given time. It is shown in this note that rank adj , where has distinct eigenvalues , is one. As a result, there are only linearly independent equations in Farlow\´s condition for the coefficients and as such only of the coefficients are determined uniquely. The other coefficients can be chosen to achieve other desirable characteristics of the system response.