On stationary inflection points in step responses

The step and impulse responses of a proper, rational transfer function are well-behaved analytic functions. We prove that such a response cannot have an inflection point such that the tangent at that point is parallel to the time-axis. Hence when a step or impulse response of a finite-dimensional LT...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Author: Maben Rabi
Format: Article
Language:English
Subjects:
Analytic functions
Impulse response
Inflection points
Transfer functions
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The step and impulse responses of a proper, rational transfer function are well-behaved analytic functions. We prove that such a response cannot have an inflection point such that the tangent at that point is parallel to the time-axis. Hence when a step or impulse response of a finite-dimensional LTI system crosses any given level, that crossing must be transversal, and can never be tangential.
ISSN:2331-8422