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

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 Laplace operator s as s=jw, where w denotes the frequency. To avoid the ill-conditioned problem, the operator w=(s-α)/(s+α) is introduced such that the system can be identified based on a state-space model in the w-operator. Then the estimated w-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 consistent estimates in the presence of measurement noise