2017/12/08 by Hoang The Tuan, Hieu Trinh, Tuan, H. T. +1
Mathematics · Engineering · Medicine · #Fractional Differential Equations Solutions #Advanced Control Systems Design #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1712.02921
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption on the existence of derivative of pseudo-states. Second, we establish fractional Lyapunov functions to fractional-order systems without the assumption on the global existence of solutions. Our theorems fill the gaps and strengthen results in some existing papers.