Minimax LQ stochastic tracking and disturbance rejection problems

An input/output approach to the minimax linear-quadratic (LQ) stochastic tracking and disturbance rejection problems is dealt with. The solution exhibits a separation property in that the corresponding two-degree-of-freedom controller is made up of a feedback part solving the underlying H_∞ mixed sensitivity problem and a feedforward part that can be evaluated independently. The solution is based on the knowledge of the reference and accessible disturbance realizations with a lead or a delay of τ or σ steps, respectively. If both τ and σ are positive and large enough, the feedforward input can be tightly approximated without requiring any stochastic modeling of the reference and the accessible disturbance