Robust H∞ filter design for discrete-time interconnected fuzzy systems with partially unknown membership functions and past output measurements

This paper is concerned with the H∞ filtering problem for discrete-time interconnected fuzzy systems with partially unknown membership functions and past output measurements. A new H∞ filter with past output measurements is designed by introducing a switching mechanism which depends on the lower and upper bounds of the unknown elements of the membership functions, and graph theory is applied to addressed the interconnections, such that the filtering error system is asymptotically stable and the desired performance is guaranteed. By using Lyapunov analysis method, H∞ filter design conditions are given in terms of convex problem constrained by linear matrix inequalities (LMI). The results of this paper extend the existing filter design methods and obtain less conservative conditions. Finally, a numerical example is given to illustrate the advantages of the proposed design method.