Abstract
Let (A,B)∈ C n×n× C n×m and let M be an (A,B)-invariant subspace. In this paper the following results are presented: (i) If dim M+ rank B⩾n, then M is stable. (ii) If M∩ Im B={0}, under some additional hypotheses, necessary and sufficient conditions for the stability of M are given. (iii) If M 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 M .
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