Some remarks on the Brunovsky canonical form

Among the various canonical forms which were proposed for constant linear systems, the one due to Brunovsky [1] certainly is the most profound. It characterizes a dynamics modulo the group of static state feedbacks by a finite set of pure integrators. Its proof, which is quite computational, has been improved in various ways, and can be found in several textbooks (see, e.g., [12, 13, 20, 21] and the references therein) We here attempt to give a more algebraic and, hopefully, more intrinsic approach It covers the time-varying case, which seems until now to have been left untouched We employ our module-theoretic framework [5], the corresponding ftitrations [3, 4 and their connections with feedbacks. The uniqueness of the controllabity indices follows at once from some associated graduation. A first draft of this result has already been presented [8].