Testing the rank of the Hankel matrix: a statistical approach

The rank of the Hankel matrix, corresponding to a system transfer function, is equal to the order of its minimal state space realization. The computation of the rank of the Hankel matrix is complicated by the fact that its block elements are rarely given exactly but are estimated instead. In this paper, we propose new statistical tests to determine the rank of the Hankel matrix. We also provide a Monte Carlo study on the reliability of these tests compared to existing procedures.