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Finite-Time Stability for interval type-2 fuzzy Nonlinear Systems via an Observer-Based Sliding Mode Control

Journal of Systems Science & Complexity 2022年第6期35卷 2223-2247页

作者： LIU Yu'an XIA Jianwei WANG Jing SHEN Hao Anhui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering Anhui University of TechnologyMa'anshan 243002China School of Mathematical Sciences Liaocheng UniversityLiaocheng 252059China School of Electrical and Information Engineering Anhui University of TechnologyMa'anshan 243002China

This work focuses on the design of a sliding mode controller for a class of continuoustime interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval.Aiming at describing the nonlinearities containing parameter uncertainties that inevitably appear in practice,the interval type-2 fuzzy sets are employed to model the studied system.To improve the designing flexibility,a fuzzy observer model non-parallel distribution compensation scheme is designed to estimate the state information of the plant,i.e.,the observer is allowed to have a mismatching premise structure from the system.On this basis,the appropriate fuzzy sliding surface and fuzzy controller are constructed by following the same premise variables as the designed fuzzy observer.Then,by means of the sliding mode control theory and the Lyapunov function method,some novel sufficient criteria are established to ensure the finite-time boundedness for the studied systems via a partitioning strategy including the reaching phase,the sliding motion phase and the whole time interval.Furthermore,the designed gains are acquired by solving the matrix convex optimization problem.Finally,the effectiveness of the developed method is demonstrated by two simulation examples.

关键词： Finite-time boundedness interval type-2 fuzzy model non-parallel distribution compensation observer-based sliding mode control

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interval type-2 fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application

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Journal of Systems Science & Complexity 2021年第6期34卷 2195-2218页

作者： LIU Xinmiao XIA Jianwei WANG Jing SHEN Hao AnHui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering Anhui University of TechnologyMa'anshan 243032China School of Mathematical Sciences Liaocheng UniversityLiaocheng 252059China School of Electrical and Information Engineering Anhui University of TechnologyMa'anshan 243002China

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.

关键词： interval type-2 fuzzy model passive filter persistent dwell-time switching rule singularly perturbed nonlinear systems

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