Fault-tolerant H_∞ filtering for fuzzy networked control systems with quantisation effects

ABSTRACT

The issue of $H_{\mathrm{\infty }}$ memory filter design is investigated for a class of discrete-time Takagi–Sugeno (T-S) fuzzy networked control systems with time-varying delay and quantisation effects. The main objective of this paper is to formulate an $H_{\mathrm{\infty }}$ memory filter that can guarantee the resulting filtering error system to be finite-time bounded. Further, by considering the communication limitations, the state signals are quantised before transmission through a logarithmic quantiser and the quantisation error is considered in the filter design. In particular, the quantisation effects are dealt by employing the generalised sector bound approach. Based on Lyapunov stability theory, novel sufficient constraints are established in the form of linear matrix inequalities, to ensure the finite-time boundedness of the augmented filtering error system. Then, a new fault-tolerant $H_{\mathrm{\infty }}$ memory filter is formulated and also the filter gain parameters are attained by solving the derived LMI based constraints. Finally, a numerical example is furnished to support the efficacy and applicability of the developed filter design.

KEYWORDS:

• Discrete-time T-S fuzzy systems
• networked control systems
• finite-time reliable filter
• quantisation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

V. Nithya

V. Nithya received her M.Sc., M.Phil., and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, TamilNadu, in 2003, 2005, and 2020, respectively. She served as a Lecturer in the Department of Mathematics, Vellalar College for Women, Erode, from 2005 to 2008. From 2008 to 2012, she was an Assistant professor at the Department of Mathematics, Tiruppur Kumaran College for Women, Tirupur, India and from 2012 to 2016, she served as an Assistant Professor in the Department of Mathematics of Angel College of Engineering and Technology, Tirupur, India. Her current research interests include dynamical systems and control theory.

R. Sakthivel

R. Sakthivel received his 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 served as 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 was a Visiting Fellow with Max Planck Institute, Magdeburg, Germany, in 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, till 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 served as an Assistant and Associate professor with the Department of Mathematics, Sungkyunkwan University, Suwon, South Korea from 2008 to 2013. From 2013 to 2016, he was a professor at the department of Mathematics, Sri Ramakrishna Institute of Technology, India. He is currently a Professor with the Department of Applied Mathematics, Bharathiar University, Coimbatore, India. He has published over 260 research papers in reputed Science Citation Index journals. His current research interests include systems and control theory, optimization techniques, and nonlinear dynamics. He has been on the Editorial Board of international journals, including the IEEE ACCESS, the Journal of the Franklin Institute, Neurocomputing, Advances in Difference equations and Journal of Electrical Engineering & Technology.

Faris Alzahrani

Faris Alzahrani received his B.Sc. degree in mathematics from King Abdulaziz University, Jeddah, Saudi Arabia in 2006,and his Ph.D. degree in mathematics from Cardiff University, Cardiff, United Kingdomin 2014. He is currently an Associate 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, control theory and dynamical systems.

Y.-K. Ma

Y.-K. Ma received his M.S. and Ph.D. degrees in Mathematics from Yonsei University, Korea, in 2007 and 2011, respectively. Soon after the completion of his Ph.D. degree, he was a Post-Doctoral Fellow at the Department of Statistics, Seoul National University, Korea from 2011 to 2012. Currently, he is an Associate Professor of Applied Mathematics at Kongju National University, Korea. His research interests include stochastic processes, control theory, and stochastic modeling.