Stability and stabilization of a class of fractional-order nonlinear systems for $$\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}$$

This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for \(0<\alpha <2\). 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 \(0<\alpha <2\) 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.