In the design of feedback control systems for linear multivariable
plants, insisting on the elimination of coupling in closed-loop is
often achieved at the expense of an increase in the multiplicity of
infinite and non-minimum phase zeros beyond those of the plant. This
behaviour is known as the ``cost of decoupling'' since these
additional zeros are manifested in the time domain by increased rise
times and undershoots in step responses. Using partially decoupling
controllers, however, it is always possible to obtain closed-loop
systems with precisely the same number of infinite and non-minimum
phase zeros as the plant, albeit at the expense of a restricted form
of transient coupling. This paper uses a generalization of the
interactor matrix to generate a class of partially decoupling
controllers for square, stable plants in which diagonal decoupling
arises as a special case, thereby permitting the designer to trade off speed of response versus the severity of transient interaction.