Robust Strict Positive Realness: New Results for Interval Plant-Controller Families

Several classical results in the systems and control field rely on strict positive realness of suitable transfer functions. Absolute stability of nonlinear systems as well as convergence and performance analysis of adaptive schemes are typical areas where strict positive realness is a key property in many problems. In this note, invariance of this property for families of perturbed transfer functions is studied. Necessary and sufficient conditions are given for strict positive realness of interval and real shifted interval plant-controller families of transfer functions.