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ABSTRACT
Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov–Krasovskii's functional and utilisation of Jensen’s inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.
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M. Syed Ali
M. Syed Ali graduated from the Department of Mathematics of Gobi Arts and Science College affiliated to Bharathiar University, Coimbatore in 2002. He received his post-graduation in Mathematics from Sri Ramakrishna Mission Vidyalaya College of Arts and Science affiliated to Bharathiar University, Coimbatore, Tamil Nadu, India, in 2005. He was awarded Master of Philosophy in 2006 in the field of Mathematics with specialized area of Numerical Analysis from Gandhigram Rural University Gandhigram, India. He was conferred with Doctor of Philosophy in 2010 in the field of Mathematics specialized in the area of Fuzzy Neural Networks in Gandhigram Rural University, Gandhigram, India. He was selected as a Post-Doctoral Fellow in the year 2010 for promoting his research in the field of Mathematics at Bharathidasan University, Trichy, Tamil Nadu and also worked there from November 2010 to February 2011. Since March 2011 he is working as Assistant Professor in Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, India. He is bestowed with the Young Scientist Award by The Academy of Sciences. He has published more than 90 research papers in various SCI journals holding impact factors. He has also published research articles in national journals and international conference proceedings. He also serves as a reviewer for several SCI journals. His research interests include stochastic differential equations, dynamical systems, fuzzy neural networks, complex networks and cryptography.
J. Yogambigai
J.Yogambigaiwas born in 1988. She received her B.Sc. degree in the field of Mathematics from Auxilium College of Arts and Science affiliated to Thiruvalluvar University, Vellore, Tamil Nadu, India, in 2011. She received M.Sc. degree in the field of Mathematics from Thiruvalluvar University, Tamil Nadu, India, in 2014. Currently she is pursuing Ph.D degree in Mathematics under the supervision of Prof. Dr. M. Syed Ali in the Department of Mathematics, Thiruvalluvar University, Tamil Nadu, India. She has published 6 research papers in various SCI journals holding impact factors. Her current research interests include pinning control, impulse control, sliding mode control, neural networks, uncertain system and complex dynamical networks.
O. M. Kwon
O. M. Kwon received the B.S. degree in Electronic Engineering from Kyungbuk national University, Daegu, Korea, in 1997, and Ph.D. degree in Electrical and Electronic Engineering from POSTECH, Pohang, Korea, in 2004. From February 2004 to January 2006, he was a senior research in Mechatronics Centre of Samsung Heavy Industries. He is currently working as a professor in School of Electrical Engineering, Chungbuk National University. His research interests include time-delay systems, cellular neural networks, robust control and filtering, large-scale systems, secure communication through synchronization between two chaotic systems, complex dynamical networks, multi-agent systems, and so on. He has been selected as one of THOMSON REUTERS 2015, 2016 and 2017 HIGHLY CITED RESEARCHERS in the field of Mathematics. He has presented more than 160 international papers in these areas. He serves as an editorial member of Neural Networks and International Journal of Control, Automation and Systems.