Exponential Stability of Fractional-Order Impulsive Control Systems With Applications in Synchronization

被引：119

作者：

Yang, Shuai ^{[1
]}

Hu, Cheng ^{[1
]}

Yu, Juan ^{[1
]}

Jiang, Haijun ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

来源：

IEEE TRANSACTIONS ON CYBERNETICS | 2020年 / 50卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Synchronization; Neural networks; Control systems; Biological system modeling; Asymptotic stability; Stability criteria; Cohen-Grossberg neural network; exponential stability; exponential synchronization; generalized Caputo fractional derivative; impulsive control; MITTAG-LEFFLER STABILITY; GROSSBERG NEURAL-NETWORKS; PROJECTIVE SYNCHRONIZATION; ACTIVATION FUNCTIONS; GLOBAL STABILITY; STABILIZATION; EXISTENCE;

D O I：

10.1109/TCYB.2019.2906497

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper investigates exponential stability of fractional-order impulsive control systems (FICSs) and exponential synchronization of fractional-order Cohen-Grossberg neural networks (FCGNNs). First, under the framework of the generalized Caputo fractional-order derivative, some new results for fractional-order calculus are established by mainly using L'Hospital's rule and Laplace transform. Besides, FICSs are translated into impulsive differential equations with fractional-order via utilizing the definition of Dirac function, which reveals that the effect of impulsive control on fractional systems is dependent of the order of the addressed systems. Furthermore, exponential stability of FICSs is proposed and some novel criteria are obtained by applying average impulsive interval and the method of induction. As an application of the stability for FICSs, exponential synchronization of FCGNNs is considered and several synchronization conditions are established under impulsive control. Finally, several numerical examples are provided to illustrate the effectiveness of the derived results.

引用

页码：3157 / 3168

页数：12

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