Stability of fractional‐order nonlinear systems by Lyapunov direct method

Abstract

In this study, by using a characterisation of functions having a fractional derivative, the authors propose a rigorous fractional Lyapunov function candidate method to analyse the stability of fractional‐order nonlinear systems. First, they prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption of the existence of the derivative of pseudo‐states. Second, they establish fractional Lyapunov functions to fractional‐order systems without the assumption of the global existence of solutions. Their theorems fill the gaps and strengthen results in some existing papers.