The mechanism of decoupling

Abstract

In the light of the concept of a decoupling vector (Stoyle and Vardulakis 19797rpar; as a minimal algebraic parametrization of a controllability subspace (c.s), the mechanism of decoupling control by state feedback is investigated. The essential equivalence of the Wonham and Morse (1970) and Falb and Wolovich (1969) solutions of the diagonal non-block restricted decoupling problem (BDP) might well be suspected and the method of decoupling vectors intertwines these so that each is seen to be crucial to the efficient formulation and solution of decoupling problems. A new formula for the classical necessary and sufficient condition given by Falb and Wolovich (1967) in terms of their B* matrix emerges naturally from the analysis. The role of decoupling c.s.s in the guise of their associated and very easily obtained decoupling vectors in solving BDP for us becomes very clear. The solution given leads to the important definition of cyclic independence for c.s.s and this is relevant to reducing other types of decoupling problems to the basic case above