Identification of closed-loop MIMO systems from time-domain data using polyspectral analysis

Identification of closed-loop MIMO (multiple-input multiple-output) linear systems given noisy input-output measurements is considered. It is assumed that the various disturbances/noise processes affecting the system are zero-mean stationary Gaussian, whereas the closed-loop system operates under an external non-Gaussian input which is not measured. Noisy measurements of the (direct) input and output of the plant are assumed to be available. Explicit parametric modeling of the various noise sequences affecting the system is not needed. In this paper a recently reported approach for SISO systems is extended to MIMO systems. First the open-loop MIMO transfer function is estimated using integrated polyspectrum and cross-polyspectrum, of the time-domain input-output measurements. Then two existing techniques for parametric system identification given consistent estimates of the underlying transfer function, are exploited. The parameter estimators are strongly consistent under certain (mild) sufficient conditions. A computer simulation example is presented to illustrate the proposed approach.