Stability, as told by its developers

The general problem of the stability of motion was introduced by A. M. Lyapunov in his memoir Lyapunov (1892), published in French in 1907 — cf. (Lyapunov, 1947), translation which was revised by Lyapunov himself. Since then, many refinements have been made by a number of authors, but confusion regarding fundamental concepts has also settled through the years. Moreover, the effect of erroneous statements has been often amplified by inexact “recursive” citations (when an author A cites an author B, based on a text written by a tertiary author C). The purpose of this article is to present basic definitions and theorems on stability, mostly on Lyapunov stability, in the form of a concise but faithful account of the original statements made by the developers of stability theory, from the Italian G. L. Lagrangia to 20th century Soviet mathematicians. To that end, we rely on original sources to transcript the exact formulations of concepts introduced in the early literature, our translations are made with a maximum of fidelity, keeping at best both the original words and the mathematical notations. We hope, with this brief historical account, to revive the interest on otherwise forgotten fundamental literature on Lyapunov stability theory.