SOS-Based Stability Analysis of Polynomial Fuzzy-Model-Based Control Systems Via Polynomial Membership Functions

This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial fuzzy-control systems, which is a generalized form of the well-known Takagi-Sugeno (T-S) FMB control systems, has been...

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Published inIEEE transactions on fuzzy systems Vol. 18; no. 5; pp. 862 - 871
Main Authors Narimani, M, Lam, H K
Format Journal Article
LanguageEnglish
Published New York IEEE 01.10.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Approximation
Control system synthesis
Control systems
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy set theory
Fuzzy systems
Lyapunov method
Mathematical analysis
Mathematical model
Mathematical models
MATLAB
Membership-functifon-shape-dependent stability conditions
polynomial fuzzy-control system
Polynomials
Stability
Stability analysis
Studies
sum of squares (SOS)
Takagi-Sugeno model
Online AccessGet full text
ISSN1063-6706
1941-0034
DOI10.1109/TFUZZ.2010.2050890

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Abstract This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial fuzzy-control systems, which is a generalized form of the well-known Takagi-Sugeno (T-S) FMB control systems, has been reported in the form of SOS-based stability conditions. Lack of information on the relations between membership functions and premise variables, in the existing stability analysis approaches, causes conservatism of their results. In this paper, to derive relaxed stability conditions for polynomial FMB control systems, membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis. Considering a polynomial FMB control system and based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived, where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller. Each product term is approximated by a polynomial. In order to obtain better approximation, the operating domain of membership functions is partitioned to subregions. Then, SOS-based stability conditions for all subregions are derived. Unlike some published stability-analysis approaches, the proposed one can be employed for stability analysis of polynomial fuzzy-control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions. The solution of the SOS-based stability conditions can be found numerically using SOSTOOLS, which is a free third-party MATLAB Toolbox. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions.
AbstractList This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial fuzzy-control systems, which is a generalized form of the well-known Takagi-Sugeno (T-S) FMB control systems, has been reported in the form of SOS-based stability conditions. Lack of information on the relations between membership functions and premise variables, in the existing stability analysis approaches, causes conservatism of their results. In this paper, to derive relaxed stability conditions for polynomial FMB control systems, membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis. Considering a polynomial FMB control system and based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived, where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller. Each product term is approximated by a polynomial. In order to obtain better approximation, the operating domain of membership functions is partitioned to subregions. Then, SOS-based stability conditions for all subregions are derived. Unlike some published stability-analysis approaches, the proposed one can be employed for stability analysis of polynomial fuzzy-control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions. The solution of the SOS-based stability conditions can be found numerically using SOSTOOLS, which is a free third-party MATLAB Toolbox. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions.
Author Narimani, M
Lam, H K
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Snippet This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability...
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SubjectTerms Approximation
Control system synthesis
Control systems
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy set theory
Fuzzy systems
Lyapunov method
Mathematical analysis
Mathematical model
Mathematical models
MATLAB
Membership-functifon-shape-dependent stability conditions
polynomial fuzzy-control system
Polynomials
Stability
Stability analysis
Studies
sum of squares (SOS)
Takagi-Sugeno model
Title SOS-Based Stability Analysis of Polynomial Fuzzy-Model-Based Control Systems Via Polynomial Membership Functions
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