Orłowski, JakubJakubOrłowskiChaillet, AntoineAntoineChailletSigalotti, MarioMarioSigalotti2024-08-142024-08-142019 IEEE2020-04IEEE Control Systems Letters2475-1456http://hdl.handle.net/10197/26574Partial stability characterizes dynamical systems for which only a part of the state variables exhibits a stable behavior. In his book on partial stability, Vorotnikov proposed a sufficient condition to establish this property through a Lyapunov-like function whose total derivative is upper-bounded by a negative definite function involving only the sub-state of interest. In this note, we show with a simple two-dimensional system that this statement is wrong in general. More precisely, we show that the convergence rate of the relevant state variables may not be uniform in the initial state. We also discuss the impact of this lack of uniformity on the connected issue of robustness with respect to exogenous disturbances.English© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Lyapunov methodsStability of nonlinear systemsJournal Article4239740110.1109/LCSYS.2019.29397172024-05-08https://creativecommons.org/licenses/by-nc-nd/3.0/ie/