Numerical computation and well-posedness of Hinfinity optimality criteria for feedback control systems

The authors outline and justify a viable method for numerical inner-outer factorization of H^infinity functions, which must be found to compute the H^infinity -optimal performance for certain control problems. Inner-outer factorization of stable transfer function can be reliably computed over a finite frequency band by numerical means, under assumptions of bounded transfer function error and bounded transfer function roll-off rate. This implies that the H^infinity -optimal weighted sensitivity problem is well-posed in an appropriate sense, contrary to the conclusions of other work in the literature. The theoretical justification for a numerical procedure for computing the factorization is presented, and its application is illustrated using an irrational transfer function. These results also present a partial answer to the question of the sufficiency of frequency response data for design purposes.