Membership-Function-Dependent Stability and Stabilization Conditions for T–S Fuzzy Time-Delay Systems

ABSTRACT

In this paper, the stability analysis and stabilization of time-delay nonlinear systems represented by a Takagi–Sugeno fuzzy model are investigated. Combining with a recently developed integral inequality, relaxed delay-dependent stability conditions are derived by means of linear matrix inequalities. To obtain the further relaxed stability criteria, the membership-function-dependent method is applied via the piecewise membership functions (PMFs) and some slack variables. The PMFs are selected to approximate the membership functions (MFs), and then the characteristics of the MFs are taken into consideration adequately. Under the imperfect premise matching design scheme, this paper also proposes a flexible fuzzy controller design strategy that the fuzzy controllers do not employ the identical MFs and the number of rules as the fuzzy models. Finally, this proposed approach is tested successfully and its effectiveness is validated by the simulation examples.

KEYWORDS:

• Imperfect premise matching
• Integral inequality
• Membership-function-dependent (MFD)
• Piecewise membership functions (PMFs)
• Takagi–Sugeno (T–S) fuzzy model
• Time-delay nonlinear systems

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (Grant: 61473239), (Grant: 51475391).

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

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 61473239], [grant number 51475391].

Notes on contributors

Kun Zhou

Kun Zhou was born in Henan Province, China in 1988. He received his BS degree in information and computing science from Zhoukou Normal University, Zhoukou, China in 2011. Now, he is pursuing PhD degree in School of Electrical Engineering at Southwest Jiaotong University, Chengdu, China. His research interests include nonlinear system control, fuzzy control and applications.

Tianmin Huang

Tianmin Huang was born in Hebei Province, China in 1958. He received his BS degree in mathematics and applied mathematics, BS degree in computational mathematics, and PhD degree in transportation management from Southwest Jiaotong University, Chengdu, China, in 1982, 1987, and 1999, respectively. He is currently a professor in School of Mathematics, Southwest Jiaotong University. His current research interests include intelligent system optimization and control, intelligent information processing and its applications in electrical system.

E-mail: [email protected]

Tao Zhao

Tao Zhao received his BS degree in mathematics and applied mathematics and PhD degree in systems engineering from Southwest Jiaotong University, Chengdu, China, in 2010 and 2015, respectively. He is currently an associate research professor in College of Electrical Engineering and Information, Sichuan University. His current research interests include type-2 fuzzy set theory and system design, rough sets, and intelligent control.

E-mail: [email protected]

Fenghua Gao

Fenghua Gao received her Bachelor of Engineering (BE) degree from Southwest Jiaotong University, Chengdu, China in 2007. She is pursuing her PhD degree in Department of Electrical Engineering at Southwest Jiaotong University in China. She was a visiting scholar to the Bradley Department of Electrical and Computer Engineering at Virginia Tech, Blacksburg, VA, USA from 2010 to 2012. Her fields of interest include data mining, power system estimation, and Wide Area Measurement applications.

E-mail: [email protected]