Invariant Description of Linear, Time-Invariant Controllable Systems

Abstract

One considers a class of linear, time-invariant controllable systems, together with a group of transformations of the systems, and one determines a complete system of independent invariants. One examines also how these invariants are influenced by a feedback. The results are also interpreted from the point of view of the canonical forms and one shows that—under some natural hypotheses—the canonical forms contained (implicitly) in the paper are described in terms of a minimal number of parameters. The algebraic concept of “universal element” is a principal tool in proving the last result and a leading guide for the whole paper.