Controllability of delay-differential systems in the behavioral approach

Linear time-invariant systems described by distributed delay-differential equations are studied from the behavioral point of view. This framework permits a clear comparison of different algebraic and analytical controllability notions, which are equivalent for systems with commensurate delays. An example is given showing that this result is false as soon as there are two noncommensurate delays. A characterization of spectral controllability for a system whose trajectories satisfy a homogeneous system of independent equations is presented, thus extends an analogous result which was known to hold for linear differential systems.