Dissipativity-Based Filtering of Time-Varying Delay Interval Type-2 Polynomial Fuzzy Systems Under Imperfect Premise Matching

This article investigates the dissipativity-based filtering problem for the nonlinear systems subject to both uncertainties and time-varying delay in the time-delay interval type-2 (IT2) polynomial fuzzy framework. Filter design is a challenging issue for complex nonlinear systems especially when uncertainties and time delay exist. The IT2 polynomial fuzzy model is an effective and powerful approach to analyze and synthesize uncertain nonlinear systems. This is the first attempt to design both the full-order and reduced-order IT2 polynomial fuzzy filter to ensure that the filtering error system is asymptotically stable under the dissipativity constraint. The design of filtering is based on the imperfect premise matching scheme where the number of fuzzy rules and shapes of membership functions of the designed fuzzy filter can differ from those of the IT2 polynomial fuzzy model, to provide greater design flexibility and lower implementation burden. By utilizing the Lyapunov–Krasovskii-functional-based approach, the information of membership functions, time delay, and system states is taken into account in the design process to develop the relaxed membership-function-dependent and delay-dependent filtering existence criteria. Finally, simulation results are presented to illustrate the effectiveness of the filtering algorithm reported in this article.