Wiener-Hopf design of optimal decoupling one-degree-of-freedom controllersfor plants with rectangular transfer matrices

This paper is a sequel to an earlier one which treated the design of optima l decoupling one-degree-of-freedom stabilizing multivariable controllers fo r plants with square transfer matrices. Here designs for plants with rectan gular transfer matrices are given which allow for feedforward compensation and more generality in the specification of the desired closed-loop transfe r matrix. As in the earlier work, all controllers are placed in the forward path of the feedback loop and non-unity feedback is permitted. The criterion for optimality is a quadratic-cost functional that penalizes both tracking error and saturation. Explicit formulas are derived which giv e the set of all those controllers that yield finite cost, as well as the o nes that are optimal. It is shown that these controllers are strictly-prope r under conditions usually prevailing in practice. The solution for plants with rectangular transfer matrices is expressed in terms of both Schur and Kronecker matrix products. When the plant transfer matrix is square, the solution reduces to the one obtained in the earlier w ork and involves only Schur matrix products.