Size reduction in four-block H∞ formulation

In this paper, some progress related to the size reduction of the H^∞ optimal controller will be presented. To reduce the order of the H^∞ optimal controller, the sizes of the state-space realizations of the rational matrices R11(s), R12(s), R21(s), and R22(s) in the four-block H^∞ optimization problem formulation are required to be small. The recently discovered properties on the solution of the algebraic Riccati equation by Postlethwaite et. al. and the pole-zero cancellation technique by Doyle and Chu will be used to construct the minimal realizations of RL1(S), RL2(S), RR1(S), and RR2(S). From these realizations, the rational matrices R11(s), R12(s), R21(s), and R22(s) can be easily obtained. Only orthogonal transformations are involved in the computation, so the algorithm is numerically reliable.