A general transfer-function approach to the discrete-time steady-state linear quadratic Gaussian stochastic control problem

Abstract

A comprehensive treatment of the discrete-time, steady-state linear quadratic Gaussian stochastic control problem which is based entirely on the z-transfer-function point of view is presented. The optimal solution is found for the general multi-variable case by exploiting the properties of the newly defined discrete generalized spectral factor. The proposed method of solution is developed independently of the results found by the time-domain approach. This method can easily cope with cases of discrete stationary coloured signals and dynamical operators in the performance index and its computational superiority over existing time-domain techniques is discussed.