Stable subspaces of matrix pairs Original Research Article

Let image and let image be an (A,B)-invariant subspace. In this paper the following results are presented: (i) If dim image rank Bgreater-or-equal, slantedn, then image is stable. (ii) If image Im B={0}, under some additional hypotheses, necessary and sufficient conditions for the stability of image are given. (iii) If image contains the controllability subspace of the pair (A,B), sufficient conditions are given in terms of the Brunovsky r-numbers and the Weyr characteristic of the eigenvalues of a quotient endomorphism associated to the noncontrollable part of the subspace image