An improved approach to fuzzy dynamic output feedback H_∞ control of continuous-time Takagi–Sugeno fuzzy systems

Abstract

This paper studies the problem of dynamic output feedback $H_{\mathrm{\infty }}$ control for continuous-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions without the special structure, a controller design method is developed and the relaxed stabilisation conditions are proposed. First, some shortcomings of the existing results are improved and a new approach is proposed for bounding the time derivatives of the membership functions. Then, less conservative conditions are obtained by introducing regulable parameters and applying the matrix decoupling techniques, which guarantee the prescribed $H_{\mathrm{\infty }}$ performance. Moreover, the relaxation technique proposed in this paper is also suitable for the fuzzy system with immeasurable premise variables. Finally, some examples are provided to demonstrate the validity of the approach.

Keywords:

• Dynamic output feedback control
• Takagi–Sugeno fuzzy systems
• $H_{\mathrm{\infty }}$ performance

Acknowledgments

The authors would like to thank the reviewers for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (61877062 and 61977043).

Notes on contributors

Guolin Hu

Guolin Hu received his B.E. degree in Mathematics and Applied Mathematics from BinZhou University in 2009 and his M.E. degree in Applied Mathematics from Nanchang Hangkong University in 2012 and his Ph.D. degree in Control Theory and Control Engineering from Dalian University of Technology in 2019. He is currently a lecturer at the School of Electrical Engineering and Automation in Qilu University of Technology. His research interests include fuzzy control and control synthesis.

Jian Zhang

Jian Zhang was born in Dezhou, Shandong Province, China in 1994. He received the B.S. degree in Electrical Engineering and Automation from Qilu University of Technology (Shandong Academy of Sciences) in 2017. Currently, he is working towards the M.S. degree at Qilu University of Technology (Shandong Academy of Sciences). His current research interest is control synthesis of T–S fuzzy systems.

Zhiguo Yan

Zhiguo Yan received his B.E. degree in Electrical Engineering and Automation from Northeast Normal University in 2005 and his M.E. degree in Control theory and Control Engineering from Qilu University of Technology in 2008 and his Ph.D. degree in Control Theory and Control Engineering from Tianjin University in 2011. He is currently a professor at the School of Electrical Engineering and Automation in Qilu University of Technology (Shandong Academy of Sciences). He is the author/coauthor of over 60 Journal papers and Conference paper. His research interests include robust control, stochastic control and robot control.