Stability of least-squares models fitted to multivariable input-output data

The stability of least-squares (LS) models fitted to input-output data from a general multivariable system is established under the assumption that the input is white. The proof presented for this property is based on purely algebraic arguments and has the virtue that it provides some expressions for the moduli of the LS model poles. These expressions are used to derive two bounds on pole moduli, which are tighter than the unity bound implied by the stability property.