Structural stability of (C, A)-marked subspaces

Given an observable pair of matrices (C, A) we consider the manifold of (C, A)-invariant subspaces having a fixed Brunovsky–Kronecker structure. Using Arnold techniques we obtain the explicit form of a miniversal deformation of a marked (C, A)-invariant subspace with respect to the usual equivalence relation. As an application, we obtain the dimension of the orbit and we characterize the structurally stable subspaces (those with open orbit).