On the relationship between minimum variance and minimum quadratic loss controllers

In the context of univariate, discrete-time, stochastic systems, the optimal polynomial based controller, in the sense of minimum output signal variance, is considered in a state-space framework. A noise-free measurement state-space model is employed in order to represent a CARMA model, and it is shown that by coupling an optimal state estimate with optimal state feedback parameters, so the minimum quadratic loss controller can be regarded as equivalent to minimum variance control. It is also shown how the optimal innovations model state estimate is not that employed in an optimal state feedback controller, a result that questions usage of the term `optimal controller´ where an innovations form of state-space model is concerned