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...

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Published in:arXiv.org 2022-06
Main Author: Maben Rabi
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Language:English
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Analytic functions
Impulse response
Inflection points
Transfer functions
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description 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.
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subjects Analytic functions
Impulse response
Inflection points
Transfer functions
title On stationary inflection points in step responses
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