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Stability Analysis and Dynamic Output Feedback Control for Nonlinear T-S Fuzzy System with Multiple Subsystems and Normalized Membership Functions

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  • Control Theory and Applications
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Abstract

This paper addresses the stability analysis and dynamic output-feedback control problems for a class of nonlinear Takagi-Sugeno (T-S) fuzzy systems with multiple subsystems and normalized membership functions. First, the switching control law of the membership function is proposed based on the membership function for the nonlinear T-S fuzzy subsystems. Secondly, the relaxation parameter is introduced into this switching control law to guarantee a minimal dwell time between two consecutive switching. Then, based on the proposed switching control law of the membership function and relaxation parameter, the dynamic output feedback controller with the estimate algorithm is designed to estimate the attraction domain. By introducing the new switched Lyapunov-Krasovskii functional, it can be seen that the solutions of the resultant closed-loop system converge to an adjustable bounded region. Compared with the previous works, the developed controller in this paper is flexible and smooth, which only uses the system output. And the results are further extended to the mobile robot case and the chemical process case. Finally, two simulation examples are performed to show the effectiveness of the theoretical results.

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Authors and Affiliations

  1. School of Electric Engineering, Yanshan University, No. 438, Haigang District, Qinhuangdao, P. R. China

    Wei Zheng, Zhi-Ming Zhang, Hong-Bin Wang & Peng-Heng Yin

  2. School of Electronic and Information Engineering, Hebei University, No. 180, 54 East Road, Baoding, P. R. China

    Hong-Rui Wang

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  1. Wei Zheng
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Correspondence to Wei Zheng.

Additional information

Recommended by Associate Editor Hongyi Li under the direction of Editor Euntai Kim. The authors are grateful to the editor and the anonymous reviewers for their valuable comments and suggestions that have helped improve the presentation of the paper. This research was financially supported by National Natural Science Foundation of China [Grant No. 61473248, 61773333]; Natural Science Foundation of Hebei Province [Grant No. F2016203496].

Wei Zheng received the M.S. degree in Institute of Electrical Engineering from Yanshan University in 2011. Currently, she is now studying Ph.D. degree of the Control Theory and Control Engineering in Yanshan University. Her current research interests include robust nonlinear control systems, control systems design over network, and intelligent control.

Zhi-Ming Zhang received the M.S. degree in Institute of Electrical Engineering from Yanshan University in 2008. Currently, he is now studying a Ph.D. degree of Control Theory and Control Engineering in Yanshan University. His research interests include robust nonlinear control and fuzzy control.

Hong-Bin Wang received the B.S. and M.S. degrees in electrical engineering and automation from Northeast National Heavy Machinery University in 1988 and 1993, respectively. Moreover, he received the Ph.D. degree in Institute of Electrical Engineering from Yanshan University in 2005. He is currently a professor in the Institute of Electrical Engineering of Yanshan University. He is the associate dean for the institute of Electrical Engineering, in 2008, and the dean of Liren institute, Yanshan University, Qinhuangdao, China, in 2016. He is the (co)author of many books, and about 60 papers, get about 10 national invention patents. As (a)an (co)-investigator, he was finished and carrying out more than 31 projects, supported by Key Construction Program of the National 863 Project; National Natural Science Foundation of China (NSFC); Natural Science Foundation of Hebei Province of China, and other important engineering project foundations where applied practically.

Hong-Rui Wang received the B.S. and M.S. degrees in electrical engineering and automation from Northeast National Heavy Machinery University, in 1979 and 1981, respectively. Moreover, He received the Ph.D. degree in Institute of Electrical Engineering from Yanshan University. He is currently a professor in the Institute of Electrical Engineering of Yanshan University. He was the vice-president of a Yanshan University (1997. 8–1999. 9). He was the headmaster of a Hebei University (1999. 9–2012. 6). He is the Party Secretary of Hebei University(2012. 6–Now). He is the (co)author of many books, and about 158 papers. He is the member of Chinese Association of Automation; executive director of China Higher Education Management Research Association; director of the Fifth Council of China Association for International Education; and executive vice president, of Hebei Higher Education Association.

Peng-Heng Yin received the B.S. degree in Institute of Electrical Engineering from Yanshan University in 2017. Currently, he is now studying his M.S. degree of Control Theory and Control Engineering in Institute of Electrical Engineering from Yanshan University. His research interests include adaptive and fuzzy control.

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Zheng, W., Zhang, ZM., Wang, HB. et al. Stability Analysis and Dynamic Output Feedback Control for Nonlinear T-S Fuzzy System with Multiple Subsystems and Normalized Membership Functions. Int. J. Control Autom. Syst. 16, 2801–2813 (2018). https://doi.org/10.1007/s12555-018-0139-1

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