LAUSR

ABSTRACT Let be the set of sequences of real matrices , , , admitting a minimal partial realisation of order d and such that the sum of their largest partial row and column Kronecker indices is smaller than or equal to n. This set is a differentiable manifold which can be stratified according to the partial row and column Kronecker indices of the sequences L. Let be the set of triples such that is controllable and is observable. This set can also be stratified according to the Brunovsky indices of controllability and observability of and , respectively. In this paper we show that this stratification is Whitney regular and from it the regularity of the considered stratification of will be proved. The study of generic families of elements in or in is also included.