A polynomial approach to the MIMO LQ servo and disturbance rejection problems

A l~ t r~e t -A novel matrix fraction solution to the discretetime LQ stochastic tracking and servo problems is extended to the disturbance rejection problem. Unlike recent contributions, here the resulting control law at time t is given in terms of an expectation conditioned to the accessible disturbance given up to time t + k. If k is positive and large enough, the optimal feedforward input can be tightly approximated without requiring any stochastic model for the disturbance. If the latter is known (also for recurrent or predictable disturbance), the optimal feedforward input is obtained by solving a single bilateral Diophatine equation.