Stability and Stabilization of a Class of Fractional-Order Nonlinear Systems for 1 < α < 2

Abstract

This study is interested in the stability and stabilization of a class of fractional-order nonlinear systems with Caputo derivatives. Based on the properties of the Laplace transform, Mittag-Leffler function, Jordan decomposition, and Grönwall's inequality, some sufficient conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with 1<α<2 are presented. Finally, typical instances, including the fractional-order three-dimensional (3D) nonlinear system and the fractional-order four-dimensional (4D) nonlinear hyperchaos, are implemented to demonstrate the feasibility and validity of the proposed method.