Design of deadbeat control system considering worst case steady-state tracking performance

This paper deals with the problem of synthesis of controllers minimizing the worst case steady-state controlled error in the presence of time-varying unstructured uncertainty. First, under the assumption that the plant is strictly proper, we present a new and simple expression for calculating the worst case steady-state error, which gives useful and interesting suggestions on the controller design. Therefore, it is revealed that the synthesis problem can be reduced to a simple and tractable l₁-norm minimization problem. Next, using this reduction, a simple design method is presented for obtaining deadbeat controllers with given settling steps to guarantee the robust stability and to minimize the worst case steady-state controlled error. The proposed controllers are obtained easily by solving a simple linear programming problem