Behavioral Controllability of Delay-Differential Systems

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