Stability analysis of nonlinear fractional-order systems with variable-time impulses

This paper aims at analyzing the stability analysis for a class of variable-time impulsive fractional order nonlinear systems. Based on the theory of fractional calculus, the theory of impulsive differential equation, inequality techniques, and the B-equivalence method, the variable-time jump operator of the considered system can be updated as a fixed-time substitution, and the fractional-order system with the latter operator can be regarded as the comparison system of the original system. In addition, both graphic illustration and theoretical explanation are presented. Finally, two numerical examples are shown to demonstrate the validity and feasibility of the obtained results. (C) 2017 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.