New LMI approach to fuzzy H∞ filter designs

Jinhui Zhang; Yuanqing Xia

doi:10.1109/TCSII.2009.2027948

New LMI approach to fuzzy H_∞ filter designs

Jinhui Zhang^*, Yuanqing Xia

^*Corresponding author for this work

School of Automation

Research output: Contribution to journal › Article › peer-review

53 Citations (Scopus)

Abstract

This brief is concerned with the H_∞ filtering problem for a class of discrete-time fuzzy systems. The objective is to find a new way to design a stable filter guaranteeing the asymptotic stability and a prescribed H_∞ performance of the filtering error system. By using the fuzzy Lyapunov function approach and adding slack matrix variables, a new condition for H_∞ performance analysis is proposed. Then, a linear matrix inequality (LMI)-based approach is developed for designing the fuzzy H_∞ filter, which can be obtained from the solution of convex optimization problems. When these LMIs are feasible, an explicit expression of a desired H_∞ fuzzy filter is given. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

Original language	English
Pages (from-to)	739-743
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems II: Express Briefs
Volume	56
Issue number	9
DOIs	https://doi.org/10.1109/TCSII.2009.2027948
Publication status	Published - 2009

Keywords

Discrete-time systems
Fuzzy Lyapunov function
H filtering
Linear matrix inequality (LMI)
Takagi-Sugeno (T-S) fuzzy model

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10.1109/TCSII.2009.2027948

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AU - Xia, Yuanqing

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AB - This brief is concerned with the H∞ filtering problem for a class of discrete-time fuzzy systems. The objective is to find a new way to design a stable filter guaranteeing the asymptotic stability and a prescribed H∞ performance of the filtering error system. By using the fuzzy Lyapunov function approach and adding slack matrix variables, a new condition for H∞ performance analysis is proposed. Then, a linear matrix inequality (LMI)-based approach is developed for designing the fuzzy H∞ filter, which can be obtained from the solution of convex optimization problems. When these LMIs are feasible, an explicit expression of a desired H∞ fuzzy filter is given. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

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KW - Linear matrix inequality (LMI)

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New LMI approach to fuzzy H_∞ filter designs

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