New LMI approach to fuzzy H∞ filter designs

  • Authors:
  • Jinhui Zhang;Yuanqing Xia

  • Affiliations:
  • Department of Automatic Control, Beijing Institute of Technology, Beijing, China;Department of Automatic Control, Beijing Institute of Technology, Beijing, China

  • Venue:
  • IEEE Transactions on Circuits and Systems II: Express Briefs
  • Year:
  • 2009

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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.