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

Authors: 

Tran Minh Duc, Ngo Van Hoa

Source title: 
Chaos, Solitons and Fractals, 153(2): 111525, 2021 (ISI)
Academic year of acceptance: 
2021-2022
Abstract: 

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.