Box, Jenkins-Ã\x85ström and Kalman linear control laws and their equivalence

A state-space equivalent of the general Box, Jenkins¿Åström single input/output, discrete stochastic-system model is given. The `noise¿ estimates from them are shown to be the same. It is suggested that equivalence of the controls, for the same cost function, follows directly; but the equivalence is also demonstrated more formally. The relation of these results to those for a model with uncorrelated system and measurement noise, and to `multistage¿ control, is also dealt with.