Direct structure identification of linear multivariable systems from operating records

A structure identification algorithm for linear multivariable systems is described that permits colored measurement and process noise as well as control inputs. An apparently new canonical form for matrix fraction descriptions (MFD), the Structure Canonical form, is used to develop the algorithm. The identification is made from operating records rather than responses to special inputs, is noniterative and is thus termed direct identification. The algorithm requires testing a noise corrupted matrix for singularity and a threshold test for singularity using singular values is developed. The results extend those of previous studies which consider white measurement and process noise and do not allow control inputs. They can be interpreted as generalizing to the multivariable case partial autocorrelation techniques used in time series analysis.