Boundary implications for interval positive rational functions

Abstract

Positive rational functions have provided the foundation supporting the realizability theory of electrical networks. In practice, it is meaningful to provide each coefficient value with a lower and an upper bound so that the interval rational functions set up be associated in parameter space by a multidimensional boxed domain. The boundary implications for the positive real (complex) property to hold for all rational functions associated with the box are formulated in terms of the validity of the same property on a small subset of the extreme functions associated with a correspondingly small subset of vertices of the box. The results, therefore, generalize recent contributions on boundary implications of stability properties and also strict positive realness. >