Equivalence between positive real and norm-bounded uncertainty

Abstract

This paper focuses on a linear time-invariant system with positive real uncertainty and shows an equivalence between positive real and norm-bounded uncertainty resulting in transformation of a proper transfer function with positive real uncertainty directly to a strictly proper transfer function with norm-bounded uncertainty which is different from the result obtained by using bilinear transform. This paper also shows a secondary result, relations between the quadratic and robust stability of a system with positive real uncertainty.