Stability Analysis of Fractional-Order Nonlinear Systems with Delay

Abstract EN

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.