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Interval type-2 fuzzy passive filtering for nonlinear singularly perturbed PDT-switched systems and its application. (English) Zbl 1485.93591

Summary: 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.

MSC:

93E11 Filtering in stochastic control theory
93C42 Fuzzy control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C70 Time-scale analysis and singular perturbations in control/observation systems
93C10 Nonlinear systems in control theory
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