The use of Laurent power series expansions of the eigenvector matrix of a linear multivariable transfer function matrix G(z) holds the kev to the physical realization of commutative controllers. In general, however, such controllers would be anti-causal. It is the purpose of this paper to show that there are enough degrees of freedom in the choice of the controller eigenfunctions both to effect gain/phase compensation of the frequency response of the eigenfunctions of G(z), and to force the resulting control law to be causal. The results of the paper are shown to be superior to those possible through the use of approximate commutative controllers proposed earlier.