Abstract :
This paper considers Jordan canonical forms for the similarity action of Gl(n, C) on arbitrary (not necessarily reachable) input-state pairs (A,B)??Cn??nxCn??m. A modified lexicographic order (??,Ck), k??N, is defined and the Jordan canonical pairs (JA, JB) are obtained as certain minimal parameter elements of the similarity orbits [(A,B)]s. For scalar systems (m=1) the canonical pairs (JA, Jb) are explicitely characterized solely in terms of the Jordan matrix JA and the column Jb itself.
