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Fuzzy Filtering for a Class of Nonlinear Systems with Feedback Uncertainties

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Abstract

This paper studies the problem of \(H_\infty \) filtering for nonlinear uncertain systems. The parameter uncertainties are assumed to be a class of feedback uncertainties. The nonlinear plant is represented by a Takagi–Sugeno fuzzy model. The paper is focused on the design of a fuzzy filter guaranteeing a prescribed \(H_\infty \) performance of the filtering error system. By introducing some slack matrix variables, a sufficient condition for the \(H_\infty \) filter design is presented in terms of solutions to a set of linear matrix inequalities. A simulation example will be given to show the efficiency of the proposed method.

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Acknowledgments

The authors would like to thank the editors and the reviewers for their very helpful comments and suggestions for improving this paper. The work of Xiao-Heng Chang was supported in part by the National Natural Science Foundation of China (Grant No. 61104071), the Program for Liaoning Excellent Talents in University, China (Grant No. LJQ2012095), and the Open Program of the Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang University, China (Grant No. 1120211415).

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Qiao, H., Li, ZM. & Chang, XH. Fuzzy Filtering for a Class of Nonlinear Systems with Feedback Uncertainties. Int. J. Fuzzy Syst. 18, 395–404 (2016). https://doi.org/10.1007/s40815-015-0074-8

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