A Sufficient Condition for Stability of Controlled Invariant Subspaces

摘要

Given a pair of matrices (A,B) we study the stability of their invariant subspaces by means of the geometry of the manifold of quadruples (A,B,S,F) where S is an (A,B)-invariant subspace and F is such that (A+BF)SS. In particular, we derive a sufficient computable condition of stability in terms of the maximal rank of a projection map defined on the above manifold, constituting a generalization of the results about stability of invariant subspaces with regard to an endomorphism.