Convex Lyapunov functions for stability analysis of fractional order systems

This study presents an inequality which can be used to analyse the stability of fractional order systems by constructing Lyapunov functions. By using the presented inequality, it is shown that the fractional order system is Mittag–Leffler stable if there is a convex and positive definite function such that its fractional order derivative is negative definite. This result generalises the existing works and gives a useful method to construct the Lyapunov function for the stability analysis of the fractional order systems. Finally, the authors illustrate the advantages of the proposed method by two examples and their numerical simulation.