In this paper the linear transformation which is used in the unified analysis of electrical machines without & commutator is considered. It is shown that, a very straightforward derivation of the so-called commutator transformation is obtained if the underlying mathematical problem is well defined and linear system theory techniques are used to reduce a set of time-varying linear differential equations to a set of time-invariant ones. This leads to a generalization of Park's transformation to an arbitrary polyphase machine, and also yields a better insight into why the usual assumptions of unified machine theory are necessary