Finite test of robust strict positive realness

Abstract

The paper is concerned with the problem of testing the robust strict positive realness (SPRness) of a family of rational functions with both the numerator and the denominator dependent on the same set of parameters. We show that this problem can be solved by using a series of Routh tables. In other words, the robust SPRness of the whole family can be tested by performing only a finite number of elementary operations (arithmetic operations, logical operations and sign tests).