Subspace based system identification with periodic excitation signals

An identification algorithm for use with data generated by periodic inputs is presented. The algorithm is based on the geometrical properties of the resulting periodic output signal and a state-space model is derived from the signal subspace of a Hankel matrix by means of a singular value decomposition. It is shown that 2n + 1 noise-free output measurements are required to identify an nth order system. The algorithm is demonstrated to be consistent when the output measurements are corrupted by zero mean noise characterized by decaying covariances. The computational complexity of the algorithm is several orders of magnitude lower than standard methods.