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A New Global Robust Exponential Stability Criterion for H∞ Control of Uncertain Stochastic Neutral-type Neural Networks with Both Timevarying Delays

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  • Control Theory and Applications
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Abstract

This paper mainly focuses on a novel H∞ control design to handle the global robust exponential stability problem for uncertain stochastic neutral-type neural networks (USNNNs) with mixed time-varying delays. Here the delays are assumed to be both discrete and distributed, which means that the lower and upper bounds can be derived. Firstly, we draw a control law for stabilized and stability of the neutral-type neural networks (NNNs). Secondly, by employing the Lyapunov-Krasovskii functional(LKF) theory, Jensen’s integral inequality, new required sufficient conditions for the global robust exponential stability of the given neural networks (NNs) are established in terms of delay-dependent linear matrix inequalities (LMIs), which can be easily checked in practice. The conditions obtained are expressed in terms of LMIs whose feasibility can be verified easily by MATLAB LMI control toolbox. Moreover, we have compared our work with previous one in the existing literature and showed that it reduces conservatism. Finally, one numerical example with their simulations is given to validate the effectiveness of our proposed theoretical results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Alagappa University, Karaikudi, 630 004, India

    Maharajan Chinnamuniyandi

  2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    Raja Ramachandran

  3. School of Mathematics, Southeast University, Nanjing, 211189, China

    Jinde Cao

  4. School of Electrical Engineering, Nantong University, Nantong, 226019, China

    Jinde Cao

  5. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand

    Grienggrai Rajchakit

  6. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, P. R. China

    Xiaodi Li

Authors
  1. Maharajan Chinnamuniyandi
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  2. Raja Ramachandran
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  3. Jinde Cao
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  4. Grienggrai Rajchakit
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  5. Xiaodi Li
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Corresponding author

Correspondence to Jinde Cao.

Additional information

Recommended by Associate Editor Ohmin Kwon under the direction of Editor Jessie (Ju H.) Park. This work was jointly supported by the Rajiv Gandhi National Fellowship under the University Grant Commission, New Delhi with (Ref. No.F1-17.1/2016-17/RGNF-2015-17-SC-TAM-21509) and the Thailand research grant fund (RSA5980019) and Maejo University.

Maharajan Chinnamuniyandi received the B.Sc. degree in Mathematics from Alagappa Govt. Arts College affiliated to Alagappa University, Karaikudi in 2012, the M.Sc. and M.Phil. degrees in Mathematics from Alagappa University, Karaikudi, Tamilnadu, India, in 2014 and 2015, respectively. He was a recipient of University rank holder award in post graduation and also recipient of University rank holder award with gold medal in M. Phil. He is currently pursuing a Ph.D. degree in Alagappa University, Karaikudi, Tamilnadu, India. His current research interests include stability theory of neural networks, complex systems, fractional-order neural networks, stochastic and impulsive dynamical systems.

Raja Ramachandran received the M.Sc., M.Phil., and Ph.D. degrees in Mathematics from Periyar University, Salem, India, in 2005, 2006 and 2011, respectively. He served as a Guest faculty at Periyar University, India, after the completion of his doctoral studies. He was the recipient of Sir.C.V. Raman Budding Innovator Award for the year 2010 from Periyar University, India. He is currently working as an Assistant Professor in Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, India. He obtained a grant from UGC for distinguished Young Scientist Award for the year 2013. His research interests include fractional differential equations, neural networks, genetic regulatory networks, robust nonlinear control, stochastic systems, stability analysis of dynamical systems, synchronization and chaos theory. He has authored and coauthored for more than 40 publications in these research areas in Science Citation Indexed Journals. He was a member of the Editorial Board for two special issues in Mathematical Problems in Engineering and also he served as a reviewer for more than 20 SCI journals.

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 School 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. Professor Cao was an Associate Editor of the IEEE Transactions on Neural Networks, the Journal of The Franklin Institute, Neurocomputing, and Differential Equations and Dynamical Systems. He is currently an Associate Editor of the IEEE Transactions on Cybernetics, the IEEE Transactions on Cognitive and Developmental Systems, the Neural Networks, Nonlinear Analysis: Modeling and Control, Mathematics and Computers in Simulation, the Advances in Difference Equations, and the Journal of Artificial Intelligence, and Soft Computing Research. 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 Innovation Award in 2017.

Grienggrai Rajchakit received the Ph.D. degree in Applied Mathematics from KMUTT, Bangkok, Thailand. He served as a lecturer at Department of Mathematics Faculty of Science Maejo University, Chiangmai Thailand. He was the recipient of Thailand Frontier author Award by Thomson Reuters Web of Science in the year 2016. His research interests include differential equations, neural networks, robust nonlinear control, stochastic systems, stability analysis of dynamical systems, synchronization and chaos theory. He has authored and coauthored for more than 70 publications in these research areas. He was a reviewer for more than 20 journals.

Xiaodi Li was born in Shandong province, 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 is currently a Professor with the Department of Mathematics, Shandong Normal University. He has authored or coauthored more than 50 research papers. He is an Academic Editor of International Journal of Applied Physics and Mathematics (SG), Applications and Applied Mathematics (USA), and British Journal of Mathematics & Computer Science (UK). His current research interests include stability theory, delay systems, impulsive control theory, artificial neural networks, and applied mathematics.

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Chinnamuniyandi, M., Ramachandran, R., Cao, J. et al. A New Global Robust Exponential Stability Criterion for H∞ Control of Uncertain Stochastic Neutral-type Neural Networks with Both Timevarying Delays. Int. J. Control Autom. Syst. 16, 726–738 (2018). https://doi.org/10.1007/s12555-017-0410-x

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