LMI-Based Stability Analysis for Fuzzy-Model-Based Control Systems Using Artificial T-S Fuzzy Model

This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Su...

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Bibliographic Details
Published inIEEE transactions on fuzzy systems Vol. 19; no. 3; pp. 505 - 513
Main Author Lam, H K
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2011
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Analytical models
Asymptotic stability
Control systems
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy set theory
linear-matrix inequality (LMI)
Lyapunov methods
Mathematical models
Numerical stability
Stability
Stability analysis
Stability criteria
staircase membership functions
Staircases
Studies
Takagi-Sugeno (T-S) fuzzy model
Online AccessGet full text
ISSN1063-6706
1941-0034
DOI10.1109/TFUZZ.2011.2116027

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Abstract This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Sugeno (T-S) fuzzy model are represented by the staircase ones. With the nice property of the staircase membership functions, it turns the set of infinite number of linear-matrix-inequality (LMI) based stability conditions into a finite one. Furthermore, the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions. The stability of the original FMB control systems is guaranteed by the satisfaction of the LMI-based stability conditions. The proposed stability analysis is applied to the FMB control systems of which the T-S fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to enhance the design flexibility of the fuzzy controller. A simulation example is given to illustrate the merits of the proposed approach.
AbstractList This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Sugeno (T-S) fuzzy model are represented by the staircase ones. With the nice property of the staircase membership functions, it turns the set of infinite number of linear-matrix-inequality (LMI) based stability conditions into a finite one. Furthermore, the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions. The stability of the original FMB control systems is guaranteed by the satisfaction of the LMI-based stability conditions. The proposed stability analysis is applied to the FMB control systems of which the T-S fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to enhance the design flexibility of the fuzzy controller. A simulation example is given to illustrate the merits of the proposed approach.
Author Lam, H K
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  surname: Lam
  fullname: Lam, H K
  email: hak-keung.lam@kcl.ac.uk
  organization: Div. of Eng., King's Coll. London, London, UK
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SubjectTerms Analytical models
Asymptotic stability
Control systems
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy set theory
linear-matrix inequality (LMI)
Lyapunov methods
Mathematical models
Numerical stability
Stability
Stability analysis
Stability criteria
staircase membership functions
Staircases
Studies
Takagi-Sugeno (T-S) fuzzy model
Title LMI-Based Stability Analysis for Fuzzy-Model-Based Control Systems Using Artificial T-S Fuzzy Model
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