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Robust H ∞ fuzzy control for discrete-time nonlinear systems

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Abstract

This paper studies the problem of robust H ∞ control for discrete-time nonlinear systems presented as Takagi—Sugeno’s fuzzy models. The generalized non-parallel distributed compensation (non-PDC) law and non-quadratic Lyapunov function is constructed by the proposed homogeneouspolynomially basis-dependent matrix function (HPB-MF for abbreviation). Based on the generalized non-PDC law and non-quadratic Lyapunov function, some linear matrix inequalities (LMIs) are obtained by exploiting the possible combinations of the basis functions. These LMIs ensure the asymptotic stability of the closed-loop system and guarantee a norm bound constraint on disturbance attenuation. In addition, it is shown that the LMIs become less conservative as the degree of HPB-MF increases. The merit of the methods presented in this paper lies in their less conservatism than other methods, as shown by a numerical example borrowed from the literature.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, China

    Li-Kui Wang

  2. Research Center of Information and Control, Dalian University of Technology, Dalian, 116024, China

    Xiao-Dong Liu

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  1. Li-Kui Wang
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  2. Xiao-Dong Liu
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Correspondence to Li-Kui Wang.

Additional information

Recommended by Editorial Board member Eun Tai Kim under the direction of Editor Young-Hoon Joo. This work is supported in part by the National Natural Science Foundation of China under Grant 60875032.

Li-Kui Wang received the Ph.D. degree in Control Theory and Control Engineering from Dalian University of Technology, Dalian, P. R. China in 2009. He is currently a full time lecturer in Nanchang Hangkong University. His research interests include fuzzy control theory and robust control.

Xiao-Dong Liu received the Ph.D. degree in Control Theory and Control Engineering from Northeastern University, Shenyang, P. R. China in 2003. He is currently a professor in Dalian University of Technology. He has proposed AFS theory and a coauthor of three books. His research interests include AFS (axiomatic fuzzy sets) theory and its applications, knowledge discovery and representations, data mining, analysis and design of intelligent control systems. Dr. Liu is a recipient of the 2002 Wufu-Zhenhua Best Teacher Award of the Ministry of Communications of People’s Republic of China.

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Wang, LK., Liu, XD. Robust H ∞ fuzzy control for discrete-time nonlinear systems. Int. J. Control Autom. Syst. 8, 118–126 (2010). https://doi.org/10.1007/s12555-010-0115-x

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