Stability of controlled invariant subspaces

Let (A,B)∈Cn×n×Cn×m(A,B)∈Cn×n×Cn×m and MM be an (A, B  )-invariant subspace. Let C(A,B)C(A,B) be the controllability subspace of the pair (A, B). IfM∩C(A,B)=M∩ImB,under additional hypotheses, necessary and sufficient conditions for the stability of the subspace MM are given.