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

Abstract A comprehensive treatment of the steady-state linear quadratic Gaussian stochastic control problem which is based on the transfer-function point of view is presented. The optimal solution is found, for the general multivariable case, by exploiting the properties of the newly defined generalized spectral factors. The exact equivalence between the results found by the time domain and the transfer-function approaches is established, even for the case of unstable systems. The proposed method of solution can easily cope with cases of stationary coloured signals, dynamical operators in the performance index and singular noise autocorrelation and control weighting matrices ; its computational superiority over existing time-domain techniques is demonstrated.