Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach

ABSTRACT

In this paper, we addressed the problem of stability analysis for a class of generalised mixed delayed neural networks by delay-partitioning approach. A novel integral inequality is developed by employing Wirtinger's integral inequality and Leibniz–Newton formula. By constructing an augmented Lyapunov–Krasovskii functional with triple and quadruple integral terms and using some standard integral inequality techniques, asymptotic stability criterion is obtained to the concerned neural networks. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered generalised neural networks are derived in terms of a dynamic system with sampling. Finally, numerical examples are given to show that the proposed method is less conservative than existing ones.

KEYWORDS:

• Delay-partitioning approach
• generalised neural networks
• time-delays
• linear matrix inequalities (LMIs)
• Lyapunov method
• sampled-data control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Department of Science and Technology (DST) [project number SR/FTP/MS-039/2011].

Notes on contributors

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 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 70 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.

N. Gunasekaran

N. Gunasekaran was born in 1987. He received his B. Sc degree in the field of Mathematics during 2006–2009 from Mahendra Arts and Science College, Namakkal affiliated to Periyar University, Salem, Tamil Nadu, India. He received his post graduation in Mathematics from Jamal Mohamed College affiliated to Bharathidasan University, Trichy, Tamil Nadu, India, during 2010–2012. He was awarded Master of Philosophy in 2014 in the field of Mathematics with specialized area of Cryptography from Bharathidasan University, Trichy, India. Currently he 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, and he is availing Junior Research Fellowship from Department of Science and Technology-Science and Engineering Research Board (DST-SERB), Government of India, New Delhi, India. His research interest is in the area of Stability Analysis, Sampled-data Control, Dynamical systems, Fuzzy neural networks and Cryptography.