A coordinate atlas of the manifold of observable conditioned invariant subspaces

Given an observable system (C, A) is an element of K-nxn x K-nxn with K = R or C, the set of (C, A)-invariant subspaces having the restricted system f ixed observability indices is a smooth manifold embedded on the correspondi ng Grassmannian. We obtain an explicit parametrization of it by means of an atlas of coordinate charts. This parametrization can be applied to solve s ome design problems related to the disturbance decoupling problem.