The properties of pole and zero locations for nondecreasing step responses

Abstract
A form of response to a step input in a physical system is the nondecreasing type, which is of interest to the circuit designer, especially when an overshoot in the step response is objectionable. The purpose of this paper is to discuss the properties of the pole and zero locations of rational system functions whose step responses are of this form. The few known properties of this nature are scattered mainly throughout the mathematical literature. These results are gathered here and presented in a unified manner. Secondly, several other results are developed that are believed to be new. In some cases, the proofs of the following theorems are merely sketched or omitted entirely when they are available in the referenced literature.