A generalization of some structural results to interconnected systems

A result similar to the structure theorem for multivariable systems is formulated for interconnected systems. It is based on a certain polynomial matrix D(s), the so-called intercontrollability matrix of the interconnected system, with which the controllability of the interconnected system is expressed. The main result then follows after the kernel of D(s) is determined; this kernel may in its turn be viewed as a generalization of the usual structure operator of multivariable systems. Finally, as an application, an example is included, to show the relevance of these results to the problem of the stabilizability of interconnected systems with linear local state-vector feedbacks