State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

Abstract

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.

Keywords:

• interval type-2 T–S fuzzy system
• regional switching fuzzy controller
• linear matrix inequalities
• state feedback control

Acknowledgements

The authors would like to thank reviewers for their valuable comments and suggestions.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 51177137], [grant number 61134001]; the Fundamental Research Funds for the Central Universities [grant number SWJTU11CX034].

Notes on contributors

Tao Zhao

Tao Zhao received his BS degree in mathematics and applied mathematics from Southwest Jiaotong University, Chengdu, China, in 2010. Now he is pursuing PhD degree in system engineering, Southwest Jiaotong University, Chengdu, China. His current research interests include type-2 fuzzy set theory and system design, rough sets, and intelligent control.

Jian Xiao

Jian Xiao received his BS and MS degrees in electrical engineering from Hunan University, and PhD degree from Southwest Jiaotong University, Chengdu in 1989. He has been a professor of electrical engineering at the Southwest Jiaotong University since 1994. He is the recipient of the leading person of science and technology in Sichuan province, the middle-aged and young expert with outstanding contributions of the Ministry of Railways, the expert with the special subsidy from the Chinese State Council, and the excellent teacher from the Ministry of Railways. He has published over 200 research works, including 4 books. His works have been cited in various journals and conference proceedings. His research interests include robust control, fuzzy systems and power electronics.