The controllability test for behaviors revisited
Abstract
It is well-know that a behavior defined by linear constant coefficient differential equations is controllable if and only if the corresponding complex polynomial matrix has constant rank over the complex field. We provide a new proof of this fundamental result. This proof is based on a unimodular transformation of the behavior. We argue that the unimodular transformation defines an injection from the behavior into the behavior defined by the Smith form. With this observation, that is interesting in its own right, the controllability test can be proved relatively easy.
