Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays

Abstract

This paper is concerned with the stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. The sampling period is assumed to be m in number, whose occurrence probabilities are given constants and satisfy Bernoulli distribution. By introducing an improved Lyapunov–Krasovskii functional with new triple integral terms and by combining both the convex combination technique and reciprocal convex technique, delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities. These linear matrix inequalities can be easily solved by using standard convex optimisation algorithms. The designed stochastic sampled data fuzzy controller gain can be obtained. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods.

Keywords:

• T-S fuzzy systems
• combined convex technique
• randomly occurring uncertainties
• stochastic sampling
• sampled-data control

Acknowledgements

The work was supported by NBHM research project No. 2/48(7)/2012/NBHM(R.P.)/R and D-II/12669.

Additional information

Notes on contributors

R. Rakkiyappan

R. Rakkiyappan received the bachelors degree in mathematics from the Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India, in 2002, the masters degree in mathematics from the PSG College of Arts and Science, Bharathiar University, Coimbatore, in 2004, and the Ph.D. degree from the Department of Mathematics, Gandhigram Rural University, Gandhigram, India, in 2011. He is currently an assistant professor with the Department of Mathematics, Bharathiar University. He has published more than 90 papers in international journals. His current research interests include qualitative theory of stochastic and impulsive systems, neural networks, and delay differential systems.

A. Chandrasekar

A. Chandrasekar was born in 1989. He received the B.Sc. degree in mathematics from Thiruvalluvar Government Arts College, Periyar University, Salem, India, in 2009, the M.Sc. degree in mathematics from Bharathiar University, Coimbatore, India, in 2011, and the M.Phil. degree from the Department of Mathematics, Bharathiar University, in 2012, where he is currently pursuing the Ph.D. degree in mathematics. He has published more than 10 papers in international journals. His current research interests include neural networks, memristor-based neural networks, stochastic, and impulsive systems.

S. Lakshmanan

S. Lakshmanan has got his B.Sc degree in the field of mathematics during 2002–2005 from Government Arts College, Salem-7. His M.Sc degree in Mathematics from Sri Ramakrishna Mission Vidyalaya College of Arts and Science affiliated to Bharathiar University, Coimbatore, Tamil Nadu, India during 2005–2007. He received the Master of Philosophy and Doctor of Philosophy from Department of Mathematics, Gandhigram Rural University, Gandhigram, Tamil Nadu, India, in 2008 and 2012. His research interests are in the field of qualitative theory of stochastic systems and Neural Networks. He was a Post-Doctoral Research Associate in Department of Electrical Engineering/Information and Communication Engineering, Yeungnam University, Kyongsan, Republic of Korea from 2012 to 2013. Now he is working as a Post-Doctoral Research Associate in Department of Mathematics, Faculty of Science, UAE University, Al-Ain 15551, UAE.