Application of numerical inner-outer factorization to computation of H∞-optimal performance

Completes the description of the numerical computation of optimal H^∞ performance for single-input/single-output plants. It was previously shown by the authors (1992) that inner-outer factorizations could be computed numerically with uniform accuracy under certain convergence conditions. In the present work, the authors go on to show that convergence of inner factors in the uniform norm leads to convergence of the computed optimal performance. This is because when the values of the plant inner factor are computed with sufficient accuracy, they are the exact values of another inner function that is uniformly close to the true inner function. Since the H^∞ performance criteria depend continuously on the inner factors, the authors conclude that computation of these criteria using numerically computed inner factors is robust. In addition, a numerical method for computing coprime factors of a plant is presented. Coprime factorization of the plant is required to compute the H^∞ optimal performance when the plant is unstable. Given a single stabilizing compensator, one can use the method described here to obtain a numerical coprime factorization to use in computing the H^∞ optimal performance