Box-Jenkins model LQG controller: design and performance

The relationship between the variances of the input and output variables of a Box-Jenkins model control system under the linear quadratic Gaussian con trol law is obtained. This relationship is generalised to the relationships between the statistics of the input and output variables under this contro l law. Formulae to calculate these statistics are derived. The statistics a re the auto-covariances and cross-covariances of the two input and output v ariable time series driven by the same Gaussian white noise. The statistics can be used to assess control loop performance.