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

LIU Xinmiao · XIA Jianwei · WANG Jing · SHEN Hao   

  1. LIU Xinmiao
    AnHui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering,Anhui University of Technology, Ma’anshan 243032, China. Email: liuxinmiao19@gmail.com.
    XIA Jianwei
    School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China.
    Email: njustxjw@126.com.
    WANG Jing
    School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China.
    Email: jingwang08@126.com.
    SHEN Hao (Corresponding author)
    AnHui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering,Anhui University of Technology, Ma’anshan 243002, China.
  • Online:2021-12-25 Published:2021-12-25

LIU Xinmiao · XIA Jianwei · WANG Jing · SHEN Hao. Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application[J]. Journal of Systems Science and Complexity, 2021, 34(6): 2195-2218.

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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