Optimal H∞ approximation by systems of prescribed order using frequency response data

A method is given for the H^∞ approximation of discrete-time systems of arbitrary order, whose frequency responses have derivatives satisfying an a priori bound and are specified only by corrupted measurements at m frequencies. The approximation is by polynomial systems of prescribed order r-1. The method is based on convex optimization. Bounds on the approximation error and its departure from optimality are derived. In certain cases the approximation approaches optimality