Membership‐function‐dependent approach to design filter for non‐linear systems with time‐varying delay via interval type‐2 fuzzy model

This paper addresses the problem of H∞ filtering for non‐linear systems with time‐varying delay via the interval type‐2 (IT2) fuzzy model and the membership‐function‐dependent approach. By taking the time‐varying delay and uncertainties into consideration, the non‐linear plant is modelled as an IT2 fuzzy delayed system, which fully captures the parameter uncertainties of the systems by using upper and lower membership functions. An IT2 fuzzy filter is designed to estimate the unknown information of the non‐linear systems, which does not require the same premise variables as the plant. By combining the IT2 fuzzy delayed system and the IT2 fuzzy filter, a filtering error system is established. Based on the Lyapunov theory, a fuzzy‐dependent Lyapunov function is constructed. Then, the membership‐function‐dependent approach, delay analysis approach, and some slack matrix variables are employing to analyse the derivative terms of the Lyapunov function, and a less conservative condition is derived to guarantee the filtering error system is stable. Moreover, the standard conditions of the filter are given in the form of linear matrix inequalities via the matrix decoupling technique. Finally, a numerical example is given to demonstrate the effectiveness and merits of the proposed method.