OPTIMAL-DESIGN OF ROBUST CONTROLLERS FOR UNCERTAIN DISCRETE-TIME-SYSTEMS

This paper presents a fast algorithm for the design of robust output f eedback controllers for linear uncertain discrete-time systems. The al gorithm utilizes a version of the Broyden-Fletcher-Goldfarb-Shanno (BF GS) optimization method of conjugate directions and minimizes a perfor mance index that includes a linear quadratic regulator (LQR) term to o ptimize performance and a robustness term based on recently developed bounds. The minimization of only the robustness term which corresponds to the maximization of the uncertainty bound is also studied. The cas e of unstructured perturbations in A has been the only one studied in the robust controller design literature; the present algorithm introdu ces a unified approach to both cases of unstructured and structured pe rturbations in the matrices of a state-space model. For the special ca se of unstructured perturbations in A only, the algorithm is shown to improve considerably the existing unstructured uncertainty bound. Seve ral examples, including an aircraft control system and a paper-machine head box, are presented to illustrate the results.