Optimal control of the linear regulator with constant disturbances

An optimal control problem for a linear regulator with constant external disturbance is formulated. It is shown that, for a suitably selected quadratic-type performance index, the optimal control is not an explicit function of the external disturbance. Moreover, the optimal control can be synthesized as a time-invariant linear function of the state plus the first time integral of a certain other time-invariant linear function of the state.