Starting from the existence of a $C^{p}$-basis for any $C^{p}$-family of subspaces having constant dimension, we construct a Brunovsky basis of class $C^{p}$ for a $C^{p}$-family of pairs of matrices having constant Brunovsky type. We derive a global pole assignment theorem for such kind of pairs. In all the cases we assume that the manifold of parameters is contractible