Graph theory based decentralized H∞ filtering for large-scale T-S fuzzy systems

This paper is concerned with the problem of decentralized H
∞
filtering for large-scale T-S fuzzy systems, where the interconnections are nonlinear and with known weights. The algebraic graph theory is used to construct a new Lyapunov function such that the effects of the nonlinear interconnections can be included in some constants related with the interconnected weights. As a result, a novel decentralized filtering scheme is derived, and the corresponding filter synthesis conditions are given in terms of the solutions of a set of linear matrix inequalities (LMIs). In contrast to the conventional filtering schemes, where the interconnections are assumed to be local linear, the proposed decentralized filter design conditions are based on fewer fuzzy rules and less computational burden. Moreover, a unified filter design framework is derived for the large-scale T-S fuzzy systems with or without time-delayed nonlinear interconnections. Finally, a simulation example is provided to illustrate the effectiveness and advantages of the theoretical results.