Frequency domain subspace model identification with the aid of the ω-operator

This paper proposes an efficient and convenient approach to frequency domain subspace identification for continuous-time systems. In the case of continuous-time models, the data matrices often become ill-conditioned if we simply rewrite the Lapalace operator s as s = j omega, where omega denotes the frequency. To avoid the ill-conditioned problem, the operator omega = (s - alpha)/(s + alpha) is introduced such that the system can be identified based on a state-space model in the omega-operator. And then the estimated omega-operator state-space model can be transformed back to the common continuous-time state-space model. An instrumental variable matrix in the frequency domain is also proposed to obtain cosistent estimates in the presence of measurement noise.