Instrumental variable frequency-domain subspace identification

In this paper, we study instrumental variable subspace identification of multi-input/multi-output linear-time-invariant, discrete-time systems from non-uniformly spaced frequency response measurements. A particular algorithm, which does not require noise covariance function to be known a priori is shown to be strongly consistent provided that disturbances have uniformly bounded second-order moments and the frequencies satisfy a certain regularity condition. Interpolation properties of this algorithm and a related one are also studied. A numerical example illustrating the properties of the studied algorithms is presented.