Frequency domain subspace model identification using the w -operator

Abstract

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