Distributed H∞ fuzzy filtering for nonlinear systems interconnected over graphs

Abstract

SummaryThis article investigates the distributed fuzzy filtering problem for a class of Takagi–Sugeno (T‐S) fuzzy model‐based nonlinear systems interconnected over an undirected graph. The system we consider consists of numbers of heterogeneous nonlinear sub‐units interconnected over an undirected graph by sensing, computing, and communicating with each other. First, the system is represented by an undirected graph, a T‐S fuzzy model‐based state‐space equation of each subsystem and an interconnection condition. Based on this model, the concepts of the well‐posedness, stability, and contractiveness for the class of systems are introduced, and the distributed fuzzy filtering problem is established. By applying membership‐dependent multi‐Lyapunov functions, a sufficient condition on the well‐posedness, stability, and contractiveness of the open‐loop plant is then derived in terms of linear matrix inequalities (LMIs). And then, a distributed fuzzy filter inheriting the interconnected structure of the plant is designed such that the filtering error system is contractive, and a sufficient condition is correspondingly given to obtain the desired fuzzy filter parameters by solving a set of LMIs. Finally, a numerical simulation is exploited to show the validity of the proposed design method.