Revisiting limits, derivatives, and the apparent need for continuity for convergence of derivatives

  • Itzhak Barkana

Abstract

Recent papers have contested the apparent need for uniform continuity when dealing with stability of nonlinear nonautonomous systems, as it seems to arise from Barbalat's Lemma. Counterexamples that were proposed to motivate the need for uniform continuity have been shown to be wrong. However, the new publications have also met opposition contesting their mere use of limits and derivatives. A more thorough analysis show that the use of even basic mathematical concepts and mathematical language may require much more attention that it usually receives, otherwise it may lead to distortions in other than simple situations. This report thus revisits some basic concepts of Calculus for a better clarification and to avoid their misuse in other than simple situations.

Published
2017-02-28