Robust H control for fuzzy systems with Frobenius norm-bounded uncertainties

Ji Chang Lo, Min Long Lin

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38 Scopus citations


In this paper, we investigate the problem of robust H performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H problems involving uncertainty and standard uncertainty-free H problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalIEEE Transactions on Fuzzy Systems
Issue number1
StatePublished - Feb 2006


  • Bounded real lemma
  • Frobenius norm
  • H control
  • Linear matrix inequality (LMI)
  • Takagi-Sugeno (T-S) fuzzy model


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