A linear programming approach to controller design

In this paper we have suggested some procedures to deal with the fixed order controller design problem. This is a long standing open problem and in our view the conspicuous lack of results on this problem has prevented modern design methods to be applicable to real world problems which do operate under the constraint of fixed order or structure. Our methods lead to simple LP formulations in which the task of the controller is to position the closed loop characteristic polynomial or a closed loop transfer function within a box in the appropriate space of coefficients. This formulation works because it draws heavily on many fundamental bounding results from the robust parametric control theory literature. Such bounds can be used to confine the closed loop root space under interval parameter uncertainty and also to achieve guaranteed and robust performance in the H^∞ sense. We believe that the techniques given here are among handful of results available at this time to address the fixed order design problem and hope that our paper will stimulate vigorous research in this important applied area of control