LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

ABSTRACT

This paper is concerned with the asymptotic stability of the Riemann–Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results.

KEYWORDS:

• Asymptotic stability
• Riemann–Liouville fractional neural networks
• Lyapunov functional method
• discrete and distributed delays

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is jointly supported by the National Natural Science Foundation of China [number 11301308], [number 11371027], [number 61573096], [number 61272530]; the Foundation of Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [number BM2017002]; the 333 Engineering Foundation of Jiangsu Province of China [number BRA2015286]; the Natural Science Foundation of Anhui Province of China [number 1608085MA14]; the Key Project of Natural Science Research of Anhui Higher Education Institutions of China [gxyqZD2016205], [KJ2015A152]; and the Natural Science Youth Foundation of Jiangsu Province of China [number BK20160660].

Notes on contributors

Hai Zhang

Hai Zhang is currently a Professor in Anqing Normal University, China. Since July 1999, he has been working in the School of Mathematics and Computation Science, Anqing Normal University, China. He received the Ph.D. degree from Anhui University, China, in 2010. From December 2012 to November 2014, he was a Postdoctoral Research Fellow at the Department of Mathematics, Southeast University, China. His current research interests include nonlinear systems, fractional-order systems, neural networks, control theory and stability theory.

Renyu Ye

Renyu Ye is currently an Associate Professor with the School of Mathematics and Computation Science, Anqing Normal University, China. She received the B.S. degree from Anqing Normal University, Anqing, China, and the M.S. degree from Anhui University, Hefei, China, in 1999 and 2006, respectively. Currently, she is working toward the Ph.D. degree at Nanjing University of Aeronautics and Astronautics, China. Her main research interests include Bias networks, cognitive neuroscience, and neural networks.

Song Liu

Song Liu is currently an Associate Professor in Anhui University, China. Since July 2001, he has been working in School of Mathematical Sciences, Anhui University , China. He received the Ph.D. degree from Anhui University in 2011. His current research interests include stability and control theory of nonlinear systems, fractional-order systems, delay systems, singular systems and synchronisation analysis of complex networks.

Jinde Cao

Jinde Cao is a Distinguished Professor, the Dean of School of Mathematics and the Director of the Research Center for Complex Systems and Network Sciences at Southeast University. From March 1989 to May 2000, he was with the Yunnan University. In May 2000, he joined the Department of Mathematics, Southeast University, Nanjing, China. From July 2001 to June 2002, he was a Postdoctoral Research Fellow at the Department of Automation and Computer-Aided Engineering, Chinese University of Hong Kong, Hong Kong. He was an Associate Editor of the IEEE Transactions on Neural Networks, Journal of the Franklin Institute, Neurocomputing, and Differential Equations and Dynamical Systems. He is an Associate Editor of the IEEE Transactions on Cybernetics, IEEE Transactions on Cognitive and Developmental Systems, Mathematics and Computers in Simulation, and Neural Networks. He is a Fellow of IEEE, a Member of the Academy of Europe, and a Fellow of Pakistan Academy of Sciences. He has been named as Highly-Cited Researcher in Mathematics, Computer Science and Engineering by Thomson Reuters. He received the National Award for Excellence in Innovation (2017).

Ahmad Alsaedi

Ahmad Alsaedi is currently a Professor in King Abdulaziz University, Saudi Arabia. He obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, and mathematical modelling. He has published several articles in peer-reviewed journals. He served as the Chairman of the mathematics department at KAU and presently he is serving as Director of the research program at KAU. Under his great leadership, this program is running quite successfully and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM International Research Group at KAU.

Xiaodi Li

Xiaodi Li is currently a Professor with the Department of Mathematics, Shandong Normal University, China. He received the B.S. and M.S. degrees from Shandong Normal University, Jinan, China, in 2005 and 2008, respectively, and the Ph.D. degree from Xiamen University, Xiamen, China, in 2011, all in applied mathematics. He has authored or co-authored more than 50 research papers. His current research interests include stability theory, delay systems, impulsive control theory, artificial neural networks, and applied mathematics.