Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay

• Published in: Signal processing Vol. 89; no. 9; pp. 1739 - 1753
• Main Authors: Wu, Ligang, Wang, Zidong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2009; Elsevier
• Subjects: [formula omitted] performance; Applied sciences; Delay; Design engineering; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Filtering; Filtration; Fuzzy; Fuzzy filtering; Fuzzy logic; Fuzzy set theory; Information, signal and communications theory; Miscellaneous; Nonlinearity; Signal and communications theory; Signal processing; Signal, noise; Stochastic systems; Telecommunications and information theory; Time delay; T–S fuzzy systems; Fuzzy filtering; H ∞ performance; T–S fuzzy systems; Time delay; Stochastic systems; Performance evaluation; Noise reduction; T-S fuzzy systems; H; Non linear phenomenon; Convex programming; Stochastic system; Time variation; Noise level; Fuzzy algorithm; Linear matrix inequality; Delay time; H infinite optimization; Fuzzy system; Filtering; H infinite control; Non linear system; Sufficient condition; performance; Signal processing; Numerical simulation; Non linear effect
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2009.03.011

This paper is concerned with the H ∞ filtering problem for nonlinear stochastic Takagi–Sugeno (T–S) fuzzy systems with time-varying delay, where the nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent filters that guarantee a prescribed noise attenuation level in an H ∞ sense. To reduce the conservatism, a delay-dependent approach developed to derive the main results in terms of linear matrix inequalities (LMIs). When the fuzzy-rule-independent filter is applied, a sufficient condition is first proposed to ensure that the filtering error system is stochastically stable with an H ∞ performance. The corresponding solvability condition for a desired fuzzy-rule-independent filter is established by casting the fuzzy-rule-independent filter design into a convex optimization problem. Then, the parallel results are obtained for the case when the fuzzy-rule-dependent filter is used, and these results have less conservatism than those for the fuzzy-rule-independent filter design case. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.