Positive Realness Conditions for a Family of Real Rational Functions with Interval Coefficients

Abstract

Necessary and sufficient conditions are derived for real rational functions with interval coefficients to be positive real or strictly positive real. In both cases, it is shown that checking positive realness or strict positive realness of only a finite number, sixteen, of functions are required to assure the same properties for the whole family. The main tools for these results are celebrated Kharitonov's theorem and its extended version, which have been paid attention to in these couple of years in association with robust stability problems.Inspections are also made into an interrelationship between the results obtained and the (extended) Kharitonov's theorems. Though a definite answer to the relationship has not yet been established, the problem, if resolved, would shed light on implications of the Kharitonov-type theorems in concrete physical systems, i.e., electrical network systems.