Stabilization of impulsive fractional-order dynamic systems involving the Caputo fractional derivative of variable-order via a linear feedback controller

This paper investigates the stability and stabilization problem of variable-order fractional nonlinear dynamic systems with impulsive effects (VO-IFNDS) via a linear feedback controller. New inequalities on the VO Caputo fractional derivatives are established in this paper, which plays an essential role in the study of the stability theory of VO-IFNDS. Based on utilizing S-procedure and analytical technique, several sufficient criteria on Mittag-Leffler stability and asymptotical stability of VO-IFNDS are presented by means of the extension of the Lyapunov direct method. Finally, numerical examples are given to show the efficiency of the proposed method.