Dissipativity-Based Reliable Interval Type-2 Fuzzy Filter Design for Uncertain Nonlinear Systems

The problem of dissipativity-based reliable fuzzy filter design for a category of uncertain nonlinear discrete-time systems is investigated based on the interval type-2 (IT2) T–S fuzzy approach. Uncertainties, which exist in considered systems, are described via adopting both lower membership functions and upper membership functions with corresponding weighting coefficients. In the design process, a vital problem, sensor failure, is taken into consideration. To improve the flexibility of filter design, an IT2 fuzzy filter model is employed, in which membership functions are different from those of the system model. Firstly, sufficient criteria are proposed to ensure the asymptotic stability with strict dissipativity of filtering error system. Following the proposed sufficient conditions, sufficient criteria for dissipative IT2 fuzzy filter design are proposed to estimate unknown system dynamics, where cone complementary linear algorithm is introduced to solve the bilinear problem. Secondly, both $$\mathcal{H}_{\infty }$$H∞ and passive IT2 fuzzy filter design algorithms are presented as extensions. Finally, simulation results are given to illustrate the effectiveness of the IT2 fuzzy reliable filtering approach proposed in this paper.