Behavioral controllability of delay-differential systems

In this paper we will prove that the system described by the delay-differential equation R(d/dt, Delta)w = 0 (with Delta the unit delay operator) is controllable if and only if the rank of R(lambda, e(-lambda)) is constant for all lambda is an element of C. This condition is compared with the existing results obtained both bg the analytic approach and by the algebraic approach to delay-differential systems.