Frequency domain conditions for strictly positive real functions

Abstract

Frequency domain conditions for strictly positive real (SPR) functions which appear in literature are often only necessary or only sufficient. This point is raised in [1], [2], where necessary and sufficient conditions in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> -domain are given for a transfer function to be SPR. In this note, the points raised in [1], I2] are clarified further by giving necessary and sufficient conditions in the frequency domain for transfer functions to be SPR. These frequency-domain conditions are easier to test than those given in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> -domain or time domain [1], [2].