Parametric Nevanlinna-Pick Interpolation Theory

We consider the robust control problem for the system with real uncertainty. This type of problem can be represented with some parameters varying between the boundaries and is formulated as parametric Nevanlinna-Pick interpolation problem in this paper. The existence of a solution for such interpolation problem depends on the positivity of the corresponding Pick matrix with elements belonging to certain intervals. The associated necessary and sufficient condition is proved so that we only need to check the positivity of the Pick matrix evaluated at the end points of such intervals instead of for the whole intervals. This result is similar to the Kharitonov theorem or edge box theorem in the robust control theory.