Multivariable deadbeat servo problem

The problem of tracking a reference vector variable from a given class is considered for discrete-time linear multi-input-output plants. The plant and the reference are both described by an input/output relation and the objective is to track exactly in a minimum number of steps. The optimal control law is shown to contain both feedback and feedforward terms and it is obtained by solving only three linear matrix polynomial equations. The design procedure is remarkably simple and efficient.