On the transfer-function matrix and controllability of cascaded systems

Rosenbrock´s formula for the transfer-function matrix of a linear constant-coefficient dynamical system is extended to the general case of a set of compatible systems of different orders connected in cascade. The results are used to give an extension of Rosenbrock´s criteria for controllability to this general case, and to give a discussion and extension of Gilbert´s theorem on the controllability and observability of cascaded systems.