Lipschitz stability of controlled invariant subspaces

Let (A,B)∈Cn×n×Cn×m and M be an (A, B)-invariant subspace. In this paper the following results are presented: (i) If M∩ImB={0}, necessary and sufficient conditions for the Lipschitz stability of M are given. (ii) If M contains the controllability subspace of the pair (A, B), sufficient conditions for the Lipschitz stability of the subspace M are given.