A comparative analysis methods for estimating domains of attraction and convergence rates with application to a magnetic levitation system

Abstract

This article presents two methods for proving local exponential stability of the equilibrium point of a nonlinear system: the Lyapunov approach and the Gronwall inequality approach. We provide detailed theorems and proofs for each method, along with examples and numerical simulations. A comparison of the two methods is given, highlighting their respective advantages and limitations. We give a comparative analysis of two fundamental approaches to stability analysis for nonlinear systems, where we examine these methods both theoretically and numerically using specific examples of a two-dimensional nonlinear system.