Kuroiwa, Yohei (Royal Inst. of Tech.), Lindquist, Anders (Royal Inst. of Tech.)

Bi-Tangential Nevanlinna-Pick Interpolation with a Complexity Constraint

Scheduled for presentation during the Regular Session "H2 and H-infinity Control II" (FrP01), Friday, July 28, 2006, 15:20−15:45, Room B2

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

A solution to the bi-tangential Nevanlinna-Pick interpolation problem with a complexity constraint is presented, which is the natural extension of the theory developed for the scalar and matrix interpolation cases. The solution can be obtained by minimizing a strictly convex functional. This optimization problem is derived in two different ways. First, this functional is derived, in a geometric way, by path integration of a one-form which defines the bi-tangential Nevanlinna-Pick Interpolation problem. In the context of the geometric derivation, it is shown that the further generalization to Kullback-Leibler-von Neumann distance of the theory of analytic interpolation with a complexity constraint is impossible. This functional is also derived in the context of duality theory in the mathematical programming. The theory is applied to a sensitivity shaping problem, and a certain choice of a free design parameter is suggested to obtain a controller of lower degree than the generic bound.