Stability and stabilization of a class of fractional-order nonlinear systems for 0<α<2

This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for 0 < α < 2 . Based on the fractional-order Lyapunov stability theorem, S-procedure and Mittag–Leffler function, the stability conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with 0 < α < 2 are proposed. Finally, typical instances, including the fractional-order nonlinear Chen system and the fractional-order nonlinear Lorenz system, are implemented to demonstrate the feasibility and validity of the proposed method.