, Volume 10, Issue 1, pp 18-31
Date: 17 May 2014

Delay-dependent Robust Stabilization and H∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delays

Abstract

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.

P. Balasubramaniam post graduated from the Department of Mathematics of Gobi Arts College affiliated to Bharathiar University, Coimbatore in 1989. He received M. Phil. and Ph. D. degrees in mathematics with specialized area of control theory from the Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu, India in 1990, and 1994, respectively. He is rendering his services as a faculty from February 1997 at Department of Mathematics, Gandhigram Rural University, Gandhigram, Tamilnadu, India, and continuing as a professor and head since November 2006. To his credit, he has published more than 100 papers in various SCI indexed journals. In 2005, he received Tamilnadu Scientist Award for the contributions to mathematical sciences.
His research interests include the areas of control theory, soft computing, and neural networks.
T. Senthilkumar received the B.Sc. and M.Sc. degrees in mathematics from Arulmigu Palani Andavar College of Arts and Culture, Palani affiliated to madurai Kamaraj University, Madurai, India in 2002 and 2004, respectively. He obtained M. Phil. degree in mathematics with specialization in control theory from the Department of Mathematics, Government Arts College, affiliated to Bharathiar University Coimbatore, Tamilnadu, India in 2007 and B.Ed. degree in mathematics at Government College of Education, Orathanadu, Tamilnadu, India affiliated to Bharathidasan University in 2008. He received the Doctor of Philosophy (Ph. D.) in 2012 in the field of mathematics with specialized area of control theory from the Department of Mathematics, Gandhigram Rural University, Gandhigram, Tamilnadu, India. Currently, he is working as a lecturer in the Department of Mathematics, Gandhigram Rural University.
His research interests include fuzzy control, stochastic system, H∞ control, robust control, filtering, and guaranteed cost control.