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

• Published in: Journal of systems science and complexity Vol. 34; no. 6; pp. 2195 - 2218
• Main Authors: Liu, Xinmiao, Xia, Jianwei, Wang, Jing, Shen, Hao
• Format: Journal Article
• Language: English
• Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.12.2021; Springer Nature B.V
• Subjects: Circuit design; Circuits; Complex Systems; Control; Dwell time; Electronic circuits; Filtration; Fuzzy set theory; Fuzzy sets; Linear matrix inequalities; Mathematical analysis; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Parameter uncertainty; Singular perturbation; Statistics; Subsystems; Switching; Systems Theory; Time dependence; Tunnel diodes; Interval type-2 fuzzy model; passive filter; singularly perturbed nonlinear systems; persistent dwell-time switching rule
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-020-0106-9

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.