Optimal control of linear time-invariant systems with polynomial-type measurable disturbances

The optimal control of a linear time-invariant multivariable system with an integral quadratic index of performance and with measurable polynomial-type disturbances occurring in both the output and state derivative is considered in the paper. It is shown that the optimal control consists of a feedback controller and a feedforward controller. The feedback controller is the same feedback controller obtained when no disturbances are present, and an explicit expression is given for the feedforward controller. Some numerical examples are included to illustrate this optimal-control result.