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Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application

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Abstract

The problem of designing a passive filter for nonlinear switched singularly perturbed systems with parameter uncertainties is explored in this paper. Firstly, the multiple-time-scale phenomenon is settled effectively by introducing a singular perturbation parameter in the plant. Secondly, the interval type-2 fuzzy set theory is employed where parameter uncertainties are expressed in membership functions rather than the system matrices. It is worth noting that interval type-2 fuzzy sets of the devised filter are different from the plant, which makes the design of the filter more flexible. Thirdly, the persistent dwell-time switching rule, as a kind of time-dependent switching rules, is used to manage the switchings among nonlinear singularly perturbed subsystems, and this rule is more general than dwell-time and average dwell-time switching rules. Next, sufficient conditions are provided for guaranteeing that the filtering error system is globally uniformly exponentially stable with a passive performance. Furthermore, on the basis of the linear matrix inequalities, the explicit expression of the designed filter can be obtained. Finally, a tunnel diode electronic circuit is rendered as an example to confirm the correctness and the validity of the developed filter.

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Author information

Authors and Affiliations

  1. AnHui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan, 243032, China

    Xinmiao Liu

  2. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, China

    Jianwei Xia

  3. School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan, 243002, China

    Jing Wang

  4. AnHui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan, 243002, China

    Hao Shen

Authors
  1. Xinmiao Liu
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  2. Jianwei Xia
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  3. Jing Wang
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  4. Hao Shen
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Corresponding author

Correspondence to Hao Shen.

Additional information

This research was supported by the National Natural Science Foundation of China under under Grant Nos. 61873002, 61703004, 61973199, the Natural Science Foundation of Anhui Province under Grant No. 1808085QA18.

This paper was recommended for publication by Editor LI Hongyi.

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Liu, X., Xia, J., Wang, J. et al. Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application. J Syst Sci Complex 34, 2195–2218 (2021). https://doi.org/10.1007/s11424-020-0106-9

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  • DOI: https://doi.org/10.1007/s11424-020-0106-9

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