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An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination

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Abstract

The problem of sampled-data control is investigated for Takagi–Sugeno (T–S) fuzzy systems with aperiodic sampling intervals based on an enhanced input-delay approach. Delay-dependent stability and stabilizability conditions for the closed-loop continuous nonuniformly sampled-data fuzzy systems are derived by constructing a novel discontinuous Lyapunov–Krasovskii (L–K) functional, which makes good use of not only the upper bound on the variable sampling interval, but also its sawtooth structure information about varying input delay often ignored in previous results. A bounding technique combined by reciprocally convex technics and linear convex combination is presented for acquiring the time derivative of the functional, wherein Jensen’s inequality and Wirtinger’s inequality are integratively employed. And a feasible solution of the obtained criterion formulated as parameterized linear matrix inequalities is ultimately conceived. A numerical example is given to show the effectiveness of the proposed method.

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Acknowledgements

The authors would like to thank the editors and the anonymous referees whose reviews and suggestions have helped in improving the presentation of this paper. The first author is also obliged to support the Outstanding Doctoral Dissertation Fund from College of Information Science and Engineering at NEU. This study is supported by the National Basic Research Program of China (2009CB320601), the National Natural Science Foundation of China (61034005, 61273027), and the National High Technology Research and Development Program of China (2012AA040104).

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University (NEU), Shenyang, 110819, P.R. China

    Feisheng Yang, Huaguang Zhang & Yingchun Wang

  2. State Key Laboratory of Synthetical Automation for Process Industries, Shenyang, Liaoning, P.R. China

    Huaguang Zhang

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  1. Feisheng Yang
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  2. Huaguang Zhang
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  3. Yingchun Wang
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Correspondence to Huaguang Zhang.

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Yang, F., Zhang, H. & Wang, Y. An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination. Nonlinear Dyn 75, 501–512 (2014). https://doi.org/10.1007/s11071-013-1080-8

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  • DOI: https://doi.org/10.1007/s11071-013-1080-8

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