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Improved Stability and Stabilization Criteria for Uncertain T–S Fuzzy Systems with Interval Time-Varying Delay via Discrete Wirtinger-Based Inequality

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Abstract

This paper introduces a discrete Wirtinger-based inequality to investigate the problem of delay-dependent stability and stabilization of uncertain T–S fuzzy systems with interval time-varying delays. By constructing a novel Lyapunov functional and applying the discrete Wirtinger-based inequality to deal with the sum terms in the derivation of the results, two delay-dependent stability criteria and a stabilization criterion are obtained in terms of matrix inequalities. Numerical examples show that the derived stability and stabilization criteria can provide a larger allowable upper delay bound than some existing results while depending on relatively less scalar decision variables.

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Acknowledgments

This work was partially supported by various grants from the National Natural Science Foundation of China under Grant 61273114; the Innovation Program of Shanghai Municipal Education Commission under Grant 14ZZ087; the Pujiang Talent Plan of Shanghai City, China under Grant 14PJ1403800; the International Corporation Project of Shanghai Science and Technology Commission under Grant 14510722500; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Natural Science Foundation of Jiangsu Province of China under Grant BK20131403; and the Science and Technology Commission of Shanghai Municipality under Grant 15JC1401900.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200072, China

    Jin Zhang, Chen Peng, Dajun Du & Min Zheng

Authors
  1. Jin Zhang
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  2. Chen Peng
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  3. Dajun Du
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  4. Min Zheng
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Correspondence to Chen Peng.

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Zhang, J., Peng, C., Du, D. et al. Improved Stability and Stabilization Criteria for Uncertain T–S Fuzzy Systems with Interval Time-Varying Delay via Discrete Wirtinger-Based Inequality. Int. J. Fuzzy Syst. 18, 784–791 (2016). https://doi.org/10.1007/s40815-015-0090-8

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  • DOI: https://doi.org/10.1007/s40815-015-0090-8

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