Further Stability Criteria for Sampled-Data-Based Interval Type-2 Fuzzy Systems via a Refined Two-Side Looped-Functional Method
You Zheng, Huaicheng Yan, Hao Zhang, Lu Zeng, Meng Wang
Abstract
This article investigates the stability and stabilization problem of aperiodic sampled-data nonlinear systems in the framework of interval type-2 (IT-2) fuzzy models. First, by introducing two adjustable parameters and splitting the sampling intervals into four nonuniform intervals, a refined two-side looped-functional method is constructed to fully utilize inner state information during the whole aperiodic sampling interval. Simultaneously, the positive definiteness constraint for the individual matrix in Lyapunov–Krasovskii functional can be further relaxed. Then, via constructing a novel fuzzy Lyapunov–Krasovskii functional (FLKF) together with a fuzzy-dependent-switching scheme, the available features of fuzzy membership functions (FMFs) can be further taken into consideration to increase the design flexibility. Consequently, the stability condition and corresponding controller design approach for aperiodic sampled-data IT-2 fuzzy systems can be obtained with less design conservatism and larger sampling intervals. Finally, two simulation examples are employed to demonstrate the validity and superiority of the proposed method.