The Equivalence among the Solutions of the H^∞ Optimal Sensitivity Computation Problem

Abstract

This paper studies the interrelationships among varied solutions to the 1-block sensitivity minimization problems. Of particular interest are the direct relationships among the Nehari-type solution, Nevanlinna-Pick interpolation solution and the skew Toeplitz theory. In spite of the obvious improtance of such relationships, their direct equivalence is not available in the literature, except rather indirect proof via Sarason's theorem. It is shown that the Pick matrix is closely related to the orthogonalization of eigenvectors of the compressed shift, which in turn leads to the equivalence relationships among these solutions.