Some new results in state space decoupling of multivariable systems. I. A link between geometric approach and matrix methods

A method based on the algorithmization of the geometric approach, using the equivalence between the maximal unobservable subspaces and the maximal (A, B)-invariant subspaces is proposed in order to solve the problem of group decoupling for linear multivariable systems. Necessary and sufficient conditions for compatibility of the maximal controllability subspaces are transformed to the necessary and sufficient conditions for the relevant maximal unobservable subspaces. On that ground, an algorithm for group decoupling, similar to that of Silverman and Payne (1971), is derived in a simple way. Conditions for group decoupling of non-completely output controllable systems are derived. A class of systems with inherent interaction is described.