Finite-time stability of fractional-order delayed Cohen–Grossberg memristive neural networks: a novel fractional-order delayed Gronwall inequality approach

Abstract

This article is dedicated to the improved approach for the finite-time stability (FTS) of fractional-order delayed Cohen–Grossberg memristive neural networks (FDCGMNNs). First, a novel delayed integer-order Gronwall inequality is established. Second, on the basis of this inequality, a novel fractional-order delayed Gronwall inequality is developed. Third, a novel FTS criterion of FDCGMNNs is derived by virtue of the novelly developed fractional-order delayed Gronwall inequality. Eventually, the effectiveness and less conservativeness of the proposed results are shown by two numerical examples.

Keywords:

• Gronwall inequality
• fractional-order
• time delay
• finite-time stability
• Cohen–Grossberg memristive neural network

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is partially supported by the National Natural Science Foundation of China under Grants 62073217, 61374030 and 61533012 and in part by the China Postdoctoral Science Foundation under Grant 2018M641991.

Notes on contributors

Feifei Du

Feifei Du received the B.S. degree in Mathematics from Changzhi University, Changzhi, China, in 2010, the M.S. degree in Pure Mathematics from Zhejiang Sci-Tech University, Hangzhou, China, in 2013 and the Ph.D. degree in Pure Mathematics from Sun Yat-sen University, Guangzhou, China, in 2018. He is working as Post-Doctoral Research Fellow in the Department of Automation, Shanghai Jiao Tong University, Shanghai, China. His current research interests include stability theory of neural networks.

Jun-Guo Lu

Jun-Guo Lu received the B.E. and Ph.D. degrees in control theory and control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1997 and 2002, respectively. From 2001 to 2003, he was Post-Doctoral Fellow with the Department of Automation, Shanghai Jiao Tong University, Shanghai, China. In 2003, he joined Shanghai Jiao Tong University, where he is currently Professor with the Department of Automation. His current research interests include nonlinear output regulation theory and applications, fractional-order control systems, robot control and multirobot coordination, machine vision, and 3-D digitalization.