本研究計畫之目的在求解2點廣義頻譜Nevanlinna-Pick插值問題，此?差值問題在求從單位開圓盤對應到單位頻譜球內之解析函?，並使函?值與導?值滿足特定插值條件，其中函?值與導?值?是2×2複?矩陣。此一問題為結合頻譜Nevanlinna-Pick以及頻譜Caratheodory-Fejer?種插值問題而得，並為建? μ 控制器合成之?學??的關鍵，雖經國際學術界研究達20?，但尚未有確?的結果。此計畫係97、98?研究計畫之延續，結合研究2點頻譜Nevanlinna-Pick以及Caratheodory-Fejer插值問題的結?，延伸處??點2×2廣義頻譜Nevanlinna-Pick插值問題；第一?研究的重點在於延伸?點問題解的求法，到建?對應的解之實現問題，並討?延伸到多插值點的相關情形；第二?則專注在解三點SNP及其對應GSNP插值問題。 The two-point generalized spectral Nevanlinna-Pick interpolation problem will be investigated in this project which is a consecutive project of previous year. The aim is to find an analytic function from the open unit disc into 2×2 open spectral unit ball such that this function satisfies certain interpolation conditions on its values and derivatives. It is obvious that this problem is to combine the spectral Nevanlinna-Pick and spectral Caratheodory-Fejer problems, and has been studies almost 20 years; which is considered as the key to build up a definitive mathematical theory for μ-synthesis. This research is the continuation of our previous project, which want to study the two-point generalized spectral Nevanlinna-Pick interpolation problem with interpolating points based on the result of our previous study on spectral Nevanlinna-Pick and spectral Caratheodory-Fejer problems. Based on the research results of our projects in 2008 and 2009, the construction and realization of the solution of the interpolation problem will be considered in the consecutive year. In the meanwhile, the extension to multiple interpolating points will also be investigated. In the second year, the research effort will focus on solving 3-point SNP interpolation problems and its corresponding GSNP problems.
