Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

ABSTRACT

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

KEYWORDS:

• Nonlinear system
• polynomial fuzzy model
• state feedback
• polynomial Lyapunov function
• global stabilisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Alireza Nasiri

Alireza Nasiri holds a Ph.D. degree from the University of Auckland, New Zealand. He is currently Assistant Professor in the Department of Electrical and Computer Engineering at Hormozgan University and vice president of Hormozgan Science and Technology Park, Iran. He received his B.Sc. and M.Sc. degrees in electrical engineering from The University of Tehran and Iran University of Science and Technology, respectively. He was a part-time Researcher in the Speech and Acoustic Signal Processing Lab, Unitec Institute of Technology, New Zealand. His research interests are nonlinear control, active noise control and fault tolerant control.

Sing Kiong Nguang

Sing Kiong Nguang received the B.E. (with first class honors) and the Ph.D. degree from the Department of Electrical and Computer Engineering of the University of Newcastle, Callaghan, Australia, in 1992 and 1995, respectively. Currently, he is a Chair Professor at the Department of Electrical and Computer Engineering, University of Auckland, Auckland, New Zealand. He has published over 300 refereed journal and conference papers on nonlinear control design, nonlinear control systems, nonlinear time-delay systems, nonlinear sampled-data systems, biomedical systems modelling, fuzzy modelling and control, biological systems modelling and control, and food and bio-product processing. He has/had served on the editorial board of a number of international journals. He is the Chief-Editor of the International Journal of Sensors, Wireless Communications and Control.

Akshya Swain

Dhafer J. Almakhles received the B.E. degree from the department of Electrical Engineering of King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, in 2006 and the Master’s (Hons.) degree from the University of Auckland, Auckland, New Zealand, in 2011. He completed his Ph.D. degree in 2016 from the University of Auckland. During his PhD, he managed to publish and submit high quality journal and conference papers and one book chapter. Currently, he is Assistant Professor at the Department of Communication and Networks Engineeringand the coordinator of renewable energy research unit, Prince Sultan University, Riyadh, Saudi Arabia. His research interests include networked, event-triggered and quantized control systems, nonlinear control system, sliding mode control and real-time implementations on FPGA.

Dhafer Almakhles

Akshya K. Swain graduated from the Department of Electrical Engineering, Veer Surendra Sai University of Technology, Burla, India with a Gold Medal and received Masters of Electronic Systems and Communication from National Institute of Technology, Rourkela, India. He was a Commonwealth Scholar in the United Kingdom from 1994 to 1996 and received Ph.D. degree from the Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K., in 1997. Currently he is working as Associate Professor of Electrical and Computer Engineering in University of Auckland, New Zealand. His research interests include nonlinear system identification and control, fault tolerant control, biomedical signal processing, sensor networks, and control applications to power system and wireless power transfer systems. He has authored/co-authored over 170 papers in different international journals and conferences. Dr. Swain is an Associate Editor of IEEE Sensors Journal and Member of the Editorial Board of International Journal of Automation and Control and International Journal of Sensors, Wireless Communications and Control.