OPTIMAL LOOP-SHAPING FOR SYSTEMS WITH LARGE PARAMETER UNCERTAINTY VIA LINEAR-PROGRAMMING

This paper describes an optimization method for designing feedback systems subject to large parameter uncertainty. Following the design philosophy of the Quantitative Feedback Theory (Horowitz and Sidi 1972, 1978) the objective is to minimize the magnitude of the open loop L(j omega) at high frequencies subject to: (a) low and intermediate-frequency bounds capturing the closed-loop robust-performance objectives; (b) universal-frequency bound on L(j omega) which limits the effects of disturbances; and (c) realization constraints on L(s) in the form of Bode's integral. This last relation is discretized at a number of frequencies and defines, together with (a) and (b), the overall set of linear constraints in a resulting linear programming optimization problem.