The bitangential Navanlinna-Pick interpolation problem: A geometric approach

The bitangential Nevanlinna-Pick interpolation problem arises in the sensitivity minimization problem of H??-optimal control theory (see [F,FD]) and has been studied in a number of publications (eg. [BH1,BH2, BR1, Fe, K, LA]). Here we review the approach from [BH1,BH2] and summarize results from [BR1] which yield an explicit realization formula (with no recursions) for the linear fractional map which parametrizes all solutions of the problem. We also indicate how one can obtain all sensitivities for stable closed loop systems with H?? norm below a prescribed tolerance directly from zero and pole data of the open loop plant for the right half plane - without recourse to explicit inner-outer factorization.