A Class of Transfer Functions With Non-Negative Impulse Response

Abstract

Presented in this note is a class of stable, minimum phase transfer functions whose impulse response is non-negative. A simple sufficiency criterion based on the relative locations of the poles and zeros characterizes the class. When the transfer function is in a factored form the sign of its impulse response may either be obtained by inspection or is inconclusive. A need for identifying such transfer functions was recently established by Jayasuriya (1989) who showed that a controller designed on the basis of maximizing a step input disturbance will reject a persistent disturbance bounded by the size of the maximized step if and only if the closed-loop system’s impulse response is of one sign.