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Robust H∞ Performance of Discrete-time Neural Networks with Uncertainty and Time-varying Delay

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  • Control Theory and Applications
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Abstract

In this paper, we are concerned with the robust H∞ problem for a class of discrete-time neural networks with uncertainties. Under a weak assumption on the activation functional, some novel summation inequality techniques and using a new Lyapunov-Krasovskii (L-K) functional, a delay-dependent condition guaranteeing the robust asymptotically stability of the concerned neural networks is obtained in terms of a Linear Matrix Inequality(LMI). It is shown that this stability condition is less conservative than some previous ones in the literature. The controller gains can be derived by solving a set of LMIs. Finally, two numerical examples result are given to illustrate the effectiveness of the developed theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellore, 632 115, Tamilnadu, India

    M. Syed Ali, K. Meenakshi & R. Vadivel

  2. School of Electrical Engineering, Chungbuk National University, Chungdae-ro 1, Cheongju, 28644, Korea

    O. M. Kwon

Authors
  1. M. Syed Ali
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  2. K. Meenakshi
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  3. R. Vadivel
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  4. O. M. Kwon
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Corresponding author

Correspondence to O. M. Kwon.

Additional information

Recommended by Associate Editor Yongping Pan under the direction of Editor Myo Taeg Lim. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1D1A109917886) and by the Brain Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2017M3C7A1044815. This work was also supported by CSIR. 25(0274)/17/EMR-II dated 27/04/2017.

M. Syed Ali graduated in 2002 and post-graduated in 2005 from Bharathiar University, India. He was conferred with Doctor of Philosophy in 2010 in Gandhigram Rural University, Gandhigram, India. Since March 2011 he is working as an Assistant Professor in Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, India. He was awarded Young Scientist Award 2016 by The Academy of Sciences, Chennai. He has published more than 85 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.

K. Meenakshi received the B.Sc. degree in 2007. She received the M.Sc. in 2011. She was awarded Master of Philosophy in the year 2012 from the Department of Mathematics, Voorhees College, Vellore, which is affiliated to the Thiruvalluvar University in 2011.Currently she is pursuing Ph.D. degree under the supervision of an Assistant Professor Dr. M. Syed Ali, in the Department of Mathematics, Thiruvalluvar University, Tamil Nadu, India.

R. Vadivel received the B.Sc., M.Sc., and M.Phil. degrees in Mathematics from Sri Ramakrishna Mission Vidyalaya College of Arts and Science affiliated to Bharathiar University, Coimbatore, Tamil Nadu, India, in 2007, 2010, and 2012, respectively. He is currently pursuing the Ph.D. degree in Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, India.

O. M. Kwon received the B.S. degree in electronic engineering from Kyungbuk National University, Daegu, Republic of Korea, in 1997, and the Ph.D. degree in electrical and electronic engineering from POSTECH, Pohang, South Korea, in 2004. He was a Senior Researcher with the Mechatronics Center of Samsung Heavy Industries, Daejeon, Republic of Korea, from 2004 to 2006. He is currently a Professor with the School of Electrical Engineering, Chungbuk National University, Cheongju, South Korea. His current 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, multiagent systems, and sampled data control. He has presented over 160 international papers in the above areas. Dr. Kwon was a recipient of the One of the Highly Cited Researchers in the field of mathematics, in 2015, 2016, and 2017. He currently serves as an Associate Editor for Neural Networks, the International Journal of Control, Automation and Systems, Journal of Institute of Control, Robotics and Systems, and Journal of Applied Mathematics and Informatics.

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Syed Ali, M., Meenakshi, K., Vadivel, R. et al. Robust H∞ Performance of Discrete-time Neural Networks with Uncertainty and Time-varying Delay. Int. J. Control Autom. Syst. 16, 1637–1647 (2018). https://doi.org/10.1007/s12555-017-0416-4

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  • DOI: https://doi.org/10.1007/s12555-017-0416-4

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