Robust non-fragile memory feedback control for multi-weighted complex dynamical networks with randomly occurring gain fluctuations

Abstract

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results.

Keywords:

• Complex dynamical networks
• stochastic synchronisation
• non-fragile memory state-feedback control
• randomly occurring gain fluctuations
• multi-weights

Disclosure statement

The authors declare that they have no known competing financial intererests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Notes on contributors

R. Sakthivel

R. Sakthivel received the B.Sc., M.Sc., M.Phil, and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, India, in 1992, 1994, 1996, and 1999, respectively. He was a Lecturer with the Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, from 2000 to 2001. From 2001 to 2003, he was a Post-Doctoral Fellow with the Department of Mathematics, Inha University, Incheon, South Korea. He visited the Max Planck Institute, Magdeburg, Germany, in August 2002. From 2003 to 2005, he was a Japan Society for the Promotion of Science Fellow with the Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Kitakyushu, Japan. He was a Research Professor with the Department of Mathematics, Yonsei University, Seoul, South Korea, until 2006. He was a Post-Doctoral Fellow (Brain Pool Program) with the Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, South Korea, from 2006 to 2008. He was an Assistant Professor and an Associate Professor with the Department of Mathematics, Sungkyunkwan University, Suwon, South Korea, from 2008 to 2013. From 2013 to 2016, he was a Professor with the Department of Mathematics, Sri Ramakrishna Institute of Technology, India. He is currently a Professor at the Department of Applied Mathematics, Bharathiar University, Coimbatore, India. His current research interests include systems and control theory, optimization techniques, and nonlinear dynamics. He has published over 400 research papers in reputed science citation indexed journals. Prof. Sakthivel has been a recipient of the One of the Highly Cited Researchers since 2017. He has been on the editorial board of international journals, including the IEEE Access, Journal of the Franklin Institute, Neurocomputing, Neural Processing Letters, Advances in Difference equations, and Journal of Electrical Engineering and Technology.

R. Sakthivel

R. Sakthivel received the B.Sc. degree in mathematics from Bharathiar University, Coimbatore, in 2005 and the M.Sc. degree in mathematics from Bharathiar University, Coimbatore, in 2007. Also, he completed the B.Ed. degree in C.S.I. Bishop Appasamy College of Education, Coimbatore, in 2008. He completed the Ph.D. degree with the Department of Mathematics, Anna University Regional Campus, Coimbatore, in 2020. His current research interests include complex dynamical networks, and robust control theory. He has published over 15 research papers in reputed Science Citation Index journals.

P. Selvaraj

P. Selvaraj received his B.Sc., M.Sc., and M.Phil. degrees in the field of Mathematics from Bharathiar University, Coimbatore, India, in 2009, 2011, and 2012, respectively. He received the Ph.D. degree in Department of Mathematics, Anna University Regional Campus, Coimbatore, Tamil Nadu, India in 2017. His current research interests are in the field of fuzzy systems, robust control, neural networks. He has published over 30 research papers in reputed Science Citation Index journals.

Faris Alzahrani

Faris Alzahrani received the B.Sc. degree in mathematics from King Abdulaziz University, Jeddah, Saudi Arabia, in 2006 and the Ph.D. degree in mathematics from Cardiff University, Cardiff, United Kingdom, in 2014. He is currently an Assistant Professor with the Department of Mathematics, King Abdulaziz University. He has authored or co-authored over 30 research papers in reputed international journals. His current research interests include differential equations, dynamical systems, and fluid mechanics.

S. Marshal Anthoni

S. Marshal Anthoni received the M.Sc., and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, India, in 1995 and 2001, respectively. Soon after the completion of his Ph.D. degree, he served as a Lecturer in the Department of Mathematics, Kumaraguru College of Technology, Coimbatore, India from 2001 to 2003. Then, from 2003 to 2004, he was a Post-Doctoral Fellow at the Department of Mathematics, Yonsei University, South Korea. After that, he worked as a Lecturer in the Department of Mathematics, Periyar University, Salem, India from 2004 to 2008. He is currently an Associate Professor of Mathematics at Anna University Regional Campus, Coimbatore, India. His research interests include control theory, neural networks, and abstract differential equations. He has published over 90 research papers in reputed science citation indexed journals.