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Robust H ∞ Control of a Class of Switching Nonlinear Systems with Time-Varying Delay Via T–S Fuzzy Model

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Abstract

This paper considers H ∞ control of a class of switching nonlinear systems with time-varying delays via T–S fuzzy model based on piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs). The systems are switching among several nonlinear systems. The Takagi and Sugeno (T–S) fuzzy model is employed to approximate the sub-nonlinear dynamic systems. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T–S fuzzy systems. Average dwell-time approach and PFLKFs methods are utilized for the stability analysis and controller design, and with free fuzzy weighting matrix scheme. Switching and control laws are obtained such that the H ∞ performance is satisfied. The conditions of stability and the control laws are given in the form of LMIs which can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example and the control of an uncertain radio-controlled (R/C) hovercraft with time-varying delay are given to demonstrate the efficiency of the proposed method.

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Acknowledgements

The work described in this paper was partially supported partly by a grant from the National Natural Science Foundation of China (Grant No. 60904004, No. 60904061), partly by the Natural Science Foundation of Jiangsu Province (Grant NO. BK2010493), partly by the Qing Lan Project, partly by a grant from the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2009J020), and partly by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No.: CityU 1353/04E).

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Authors and Affiliations

  1. College of Information Engineering, Chengdu University of Technology, Chengdu, 610059, P.R. China

    Ou Ou

  2. Centre for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China

    Yanbing Mao, Hongbin Zhang & Liangliang Zhang

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  1. Ou Ou
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  2. Yanbing Mao
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  3. Hongbin Zhang
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  4. Liangliang Zhang
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Correspondence to Yanbing Mao.

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Ou, O., Mao, Y., Zhang, H. et al. Robust H ∞ Control of a Class of Switching Nonlinear Systems with Time-Varying Delay Via T–S Fuzzy Model. Circuits Syst Signal Process 33, 1411–1437 (2014). https://doi.org/10.1007/s00034-013-9702-4

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