Stability analysis and controller design of interval type-2 fuzzy systems with time delay

Abstract

The type-2 fuzzy models can handle the system uncertainties directly based on the type-2 fuzzy sets. In this paper, the Takagi–Sugeno fuzzy model approach is extended to the stability analysis and controller design for interval type-2 (IT2) fuzzy systems with time-varying delay. Delay-dependent robust stability criteria are developed in terms of linear matrix inequalities by using the improvement technique of free-weighting matrices. Less conservative results are obtained by considering the information contained in the footprint of uncertainty. Finally, two simulation examples are presented to illustrate the effectiveness of the theoretical results. One is provided to show the merits of the proposed method, the other based on the continuous stirred tank reactor model is given to illustrate the design processes of IT2 fuzzy controller for a nonlinear system with parameter uncertainties.

Keywords:

• type-2 fuzzy system
• stability analysis
• time delay
• system uncertainty

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 60871094), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China and the Fundamental Research Funds for the Central Universities of China.

Additional information

Notes on contributors

Long Sheng

Long Sheng received the BS degree in electronic information science and technology from the Central South University (CSU), Changsha, China, in 2004, and the MS and PhD degrees in circuit and systems from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2008 and 2012. He is currently a Research Assistant in the School of Information Science and Electrical Engineering, Hebei University of Engineering. His research interests include pattern recognition, application of fuzzy set theory and clustering techniques.

Xiaoyu Ma

Xiaoyu Ma received the BS degree from Dalian Jiaotong University, Dalian, China, in 2004, and the MS degree from Dalian University of Technology, Dalian, China, in 2008. She is currently a Research Assistant in the School of Civil Engineering, Hebei University of Engineering. Her research interests include statistical signal processing techniques, fuzzy systems and pattern recognition.