About a property of a class of linear time-varying systems derived from the controllability and observability matrices

This correspondence deals with an application of a theorem of Silverman and Meadows which specifies conditions for time-variable -dimensional vectors to be linearly dependent. From this theorem conditions are derived which allow one to verify whether a linear time-varying system admits a realization in which either the state matrix and the state-input matrix , or the state matrix and the state-output matrix , are constant.