English

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

R2 v1 2026-06-24T11:31:44.550Z