Closed-loop shaping by analytic functions with a bounded degree

This paper proposes a new technique for frequency shaping of the closed-loop system. The technique does not involve any weighting function for shaping, which is often used in the conventional H^∞ control theory, but selects a desirable analytic function from a set of H^∞ suboptimal solutions with a bounded degree. The Nevanlinna-Pick interpolation theory with a degree bound plays a central role in deriving shaping strategies of the closed-loop frequency responses. One example illustrates the efficiency of the proposed method by comparing it with a conventional method in H^∞ control.