Further results on the pointwise controllability of delay-differential systems

By expressing the recursive matrices in the controllability matrix of the delay-differential systems in terms of the sums of the two system matrices and their powers, a different controllability matrix is obtained. When the first system matrix takes the companion form and the sum of the two system matrices also takes the companion form, the controllability condition is expressed in terms of relative primeness of polynomials by means of our first result and previous results in time-invariant systems.