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

Ji Chang Lo; Min Long Lin

doi:10.1109/TFUZZ.2005.861602

Robust H_∞ control for fuzzy systems with Frobenius norm-bounded uncertainties

Ji Chang Lo, Min Long Lin

Department of Mechanical Engineering

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

38 Scopus citations

Abstract

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 language	English
Pages (from-to)	1-15
Number of pages	15
Journal	IEEE Transactions on Fuzzy Systems
Volume	14
Issue number	1
DOIs	https://doi.org/10.1109/TFUZZ.2005.861602
State	Published - Feb 2006

Keywords

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

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10.1109/TFUZZ.2005.861602

Cite this

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abstract = "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.",

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note = "Funding Information: Manuscript received July 10, 2001; revised July 30, 2002; May 30, 2003, and April 19, 2005. This work was supported by the National Science Council of the R.O.C. under Grant NSC-89-2213-E-008-075. J.-C. Lo is with the Faculty of Mechanical Engineering, National Central University, Chung-Li 320, Taiwan (e-mail: jclo@cc.ncu.edu.tw). M.-L. Lin is with the Electrical Engineering Department 1, Product Design Division 1, LITE-ON IT Corporation, Taipei 114, Taiwan. Digital Object Identifier 10.1109/TFUZZ.2005.861602",

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AB - 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.

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