Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

Xiaozhan Yang; Hak-Keung Lam; Ligang Wu

doi:10.1016/j.fss.2018.01.018

Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

Xiaozhan Yang^*, Hak-Keung Lam, Ligang Wu

^*Corresponding author for this work

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

47 Citations (Scopus)

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Abstract

This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.

Original language	English
Journal	Fuzzy Sets and Systems
Early online date	3 Feb 2018
DOIs	https://doi.org/10.1016/j.fss.2018.01.018
Publication status	E-pub ahead of print - 3 Feb 2018

Keywords

Stability analysis
T–S fuzzy system
Membership function
Convex polyhedron

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10.1016/j.fss.2018.01.018

Membership-Dependent Stability Conditions_YANG_Publishedonline3February2018_GREEN AAMAccepted author manuscript, 718 KBLicence: CC BY-NC-ND
Membership-dependent stability conditions for type-1 and interval type-2 T-S fuzzy systemsAccepted author manuscript, 791 KB

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abstract = "This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.",

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AU - Wu, Ligang

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AB - This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.

KW - Stability analysis

KW - T–S fuzzy system

KW - Membership function

KW - Convex polyhedron

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SN - 0165-0114

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -

Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

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