Matrix fraction solution to the discrete-time LQ stochastic tracking and servo problems

A novel matrix fraction solution to the discrete-time LQ (Linear quadratic) stochastic tracking and servo problems is presented. The resulting control law is based on the knowledge, at time t, of the output reference up to time t+γ. If γ is positive and large enough, the optimal feedforward input can be tightly approximated without requiring any stochastic model for the reference. If the latter is known, the optimal feedforward input is obtained by solving a bilateral Diophantine equation