Abstract
In this paper, stochastic stability is analyzed for a class of discrete-time switched neural networks, in which time-varying mixed delays and stochastic noise are considered. Specifically, benefitting from the triple summation term included in a new Lyapunov functional, time-varying distributed delays are tackled and a criterion of decay estimation for a non-switched neural network is firstly obtained. Subsequently, in view of average dwell time methodology and stochastic analysis, several sufficient conditions are obtained to ensure that the stochastic stability problem is solvable. Furthermore, the derived sufficient conditions reflect that the decay rate of the considered neural networks has a close relationship with average dwell time, upper and lower bounds of delays and intensity of stochastic noise. Finally, validity of the inferred conclusions is given by a simulated example.
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Recommended by Associate Editor M. Chadli under the direction of Editor Myo Yaeg Lim. The work is supported by National Natural Science Foundation of China under Grants 61773017, 61374010, 61503328, 11671008, Innovation Projects in Jiangsu Province (KYCX17-1873) and Top Talent Plan of Yangzhou University.
Ying Cui received the M.S. degree in 2007 from Wuhan University, Hubei, China. Now she is pursuing the Ph.D. degree in Mathematics at Yangzhou University, Jiangsu, China. Her research interests include hybrid systems, dynamics of complex networks.
Yurong Liu was born in China in 1964. He received his B.Sc. degree in Mathematics from Suzhou University, Suzhou, China, in 1986, the M.Sc. degree in Applied Mathematics from Nanjing University of Science and Technology, Nanjing, China, in 1989, and the Ph.D. degree in Applied Mathematics from Suzhou University, Suzhou, China, in 2001. Dr. Liu is currently a professor with the Department of Mathematics at Yangzhou University, China. He also serves as an Associate Editor of Neurocomputing. So far, he has published more than 50 papers in refereed international journals. His current interests include stochastic control, neural networks, complex networks, nonlinear dynamics, time-delay systems, multi-agent systems, and chaotic dynamics.
Wenbing Zhang received the M.S. degree in applied mathematics from Yangzhou University, Jiangsu, China, and the Ph.D. degree in pattern recognition and intelligence systems from Donghua University, Shanghai, China, in 2009 and 2012, respectively. He was a Research Associate with The Hong Kong Polytechnic University, Kowloon, Hong Kong, from 2012 to 2013. From July 2014 to Aug 2014, he was a DAAD fellow with the Potsdam Institute for Climate Impact Research, Potsdam, Germany. He is currently an associated professor with the Department of Mathematics, Yangzhou University. His current research interests include synchronization/consensus, networked control systems, and genetic regulatory networks. Dr. Zhang is a very active reviewer for many international journals.
Fuad E. Alsaadi received the BS and MSc degrees in Electronic and Communication from King AbdulAziz University, Jeddah, Saudi Arabia, in 1996 and 2002. He then received the PhD degree in Optical Wireless Communication Systems from the University of Leeds, Leeds, UK, in 2011. Between 1996 and 2005, he worked in Jeddah as a communication instructor in the College of Electronics & Communication. He was a lecturer in the Faculty of Engineering in King AbdulAziz University, Jeddah, Saudi Arabia in 2005. He is currently an assistant professor of the Electrical and Computer Engineering Department within the Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia. He published widely in the top IEEE communications conferences and journals and has received the Carter award, University of Leeds for the best PhD. He has research interests in optical systems and networks, signal processing, synchronization and systems design.
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Cui, Y., Liu, Y., Zhang, W. et al. Stochastic Stability for a Class of Discrete-time Switched Neural Networks with Stochastic Noise and Time-varying Mixed Delays. Int. J. Control Autom. Syst. 16, 158–167 (2018). https://doi.org/10.1007/s12555-016-0778-z
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DOI: https://doi.org/10.1007/s12555-016-0778-z