Differentiable structure of realizable Markov parameters

The geometry of the finite sequences of p × m matrices that are realizable by systems of minimal order d is investigated. They can be stratified according to their partial row and column Kronecker indices. The case when the sum of the number of non-zero row and column indices is smaller than the number of elements in the sequence of parameters is considered. It is shown that, in this case, the whole set of Markov parameters and each stratum can be endowed with structures of differentiable manifolds, and their dimensions are computed.