Stability Analysis of Fractional‐Order Nonlinear Systems with Delay

Stability analysis of fractional‐order nonlinear systems with delay is studied. We propose the definition of Mittag‐Leffler stability of time‐delay system and introduce the fractional Lyapunov direct method by using properties of Mittag‐Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional‐order nonlinear system with delay are proposed firstly. And the application of Riemann‐Liouville fractional‐order systems is extended by the fractional comparison principle and the Caputo fractional‐order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.