Delay-dependent H∞ filtering for discrete-time fuzzy stochastic systems with mixed delays and sector-bounded nonlinearity

• Published in: Journal of the Franklin Institute Vol. 352; no. 8; pp. 3069 - 3097
• Main Authors: Hua, Mingang, Cai, Yixi, Ni, Jianjun, Fei, Juntao
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2015
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2014.11.009

The delay-dependent H∞ filter problem for discrete-time Takagi–Sugeno (T–S) fuzzy stochastic systems with mixed delays and sector-bounded nonlinearity is considered in this paper. The mixed delays consist of both discrete and distributed delays, and the nonlinearity under consideration is subject to sector-bounded condition. Both the the fuzzy-rule-dependent and fuzzy-rule-independent filters are considered. Based on discrete Jensen inequality and the Lyapunov–Krasovskii functional approach combined with the S-procedure, sufficient conditions for the existence of admissible filters are established in terms of linear matrix inequalities (LMIs), which ensure the asymptotical mean-square stability as well as a prescribed H∞ performance. Finally, numerical examples are given to demonstrate the effectiveness and less conservatism of the proposed approach.