The topology of the set of conditioned invariant subspaces

We consider the topology of the set of conditioned invariant subspaces of a n observable pair (C,A) of a fixed dimension, By fixing the observability i ndices of the restricted system, a stratification by finitely many smooth m anifolds is obtained, termed Brunovsky strata. It is shown that each Brunov sky stratum is homotopy equivalent to a generalized flag manifold. From thi s description an effective formula for the Betti numbers of the Brunovsky s trata can be derived. (C) 2000 Elsevier Science B.V. All rights reserved.