Stability of multivariable least-squares models: a solution via spectral analysis

Time-domain least-squares equation-error models are widely used for estimation of an input-output (I/O) parametric transfer function. It is known that an autoregressive constraint on the input is sufficient to ensure stability of the estimated multivariable model. In this letter, we consider a frequency-domain solution to the least-squares equation-error multivariable system identification problem using the power spectrum and the cross-spectrum of the I/O data to estimate the I/O parametric transfer function. The considered approach is shown to yield stable fitted multivariable models for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order.