Identification of Minimal Order State-Space Models from Stochastic Input-Output Data

This paper discusses the problem of identifying a minimal order state space representation of a multivariable linear time invariant sytem from Gaussian stationary input-output measurements. A procedure for identifying the system´s order is proposed, based on an approximate probability distribution of the squared singular values of the Hankel matrix built from the sample cross-covariances. The approximate distribution converges to the true one as the number of measurements becomes large. The order determination procedure also identifies sets of linearly independent rows and linearly independent columns of the Hankel correlation matrix which forms a basis for a minimal order representation of the system.