Decentralised H_∞ filtering of interconnected discrete-time fuzzy systems with time delays

Abstract

This article considers the decentralised H _∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H _∞ filter is designed for each subsystem. It is shown that the stability with H _∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.

Keywords:

• decentralised
• H _∞ filter
• interconnected system
• time-delay
• Takagi–Sugeno fuzzy system

Acknowledgements

The work described in this article was supported by a grant from GRF: CityU 113308 of the Government of Hong Kong SAR, the National Natural Science Foundation of China (Grant No. 60904004), the fundamental research funds for the central universities, the Key Youth Science and Technology Foundation of University of Electronic Science and Technology of China (No. L08010201JX0720). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.