On stationary inflection points in step responses
Optimization and Control
2022-06-16 v3 Systems and Control
Systems and Control
Abstract
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.
Cite
@article{arxiv.2205.14372,
title = {On stationary inflection points in step responses},
author = {Maben Rabi},
journal= {arXiv preprint arXiv:2205.14372},
year = {2022}
}
Comments
The Theorems as stated are false