Graphical L2-stability analysis of Takagi-Sugeno control systems in the frequency domain

Xiaojun Ban; X. Z. Gao; Xianlin Huang

doi:10.1016/j.fss.2011.01.012

Graphical L₂-stability analysis of Takagi-Sugeno control systems in the frequency domain

Xiaojun Ban^*
, X. Z. Gao
, Xianlin Huang

^*Corresponding author for this work

School of Astronautics

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

2 Scopus citations

Abstract

In this paper, the upper bound of the L₂-gain of the continuous-time SISO Takagi-Sugeno (T-S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L ₂-gain, the L₂-stability of the above T-S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L₂-stability of certain kind of T-S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L₂-stability of the simplified continuous-time T-S fuzzy system can be graphically examined.

Original language	English
Pages (from-to)	93-105
Number of pages	13
Journal	Fuzzy Sets and Systems
Volume	171
Issue number	1
DOIs	https://doi.org/10.1016/j.fss.2011.01.012
State	Published - 16 May 2011

Keywords

Circle criterion
Frequency response methods
Graphical L-stability analysis
Small gain theorem
Takagi-Sugeno (T-S) fuzzy control systems

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10.1016/j.fss.2011.01.012

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title = "Graphical L2-stability analysis of Takagi-Sugeno control systems in the frequency domain",

abstract = "In this paper, the upper bound of the L2-gain of the continuous-time SISO Takagi-Sugeno (T-S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L 2-gain, the L2-stability of the above T-S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L2-stability of certain kind of T-S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T-S fuzzy system can be graphically examined.",

keywords = "Circle criterion, Frequency response methods, Graphical L-stability analysis, Small gain theorem, Takagi-Sugeno (T-S) fuzzy control systems",

author = "Xiaojun Ban and Gao, \{X. Z.\} and Xianlin Huang",

year = "2011",

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T1 - Graphical L2-stability analysis of Takagi-Sugeno control systems in the frequency domain

AU - Ban, Xiaojun

AU - Gao, X. Z.

AU - Huang, Xianlin

PY - 2011/5/16

Y1 - 2011/5/16

N2 - In this paper, the upper bound of the L2-gain of the continuous-time SISO Takagi-Sugeno (T-S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L 2-gain, the L2-stability of the above T-S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L2-stability of certain kind of T-S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T-S fuzzy system can be graphically examined.

AB - In this paper, the upper bound of the L2-gain of the continuous-time SISO Takagi-Sugeno (T-S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L 2-gain, the L2-stability of the above T-S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L2-stability of certain kind of T-S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T-S fuzzy system can be graphically examined.

KW - Circle criterion

KW - Frequency response methods

KW - Graphical L-stability analysis

KW - Small gain theorem

KW - Takagi-Sugeno (T-S) fuzzy control systems

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U2 - 10.1016/j.fss.2011.01.012

DO - 10.1016/j.fss.2011.01.012

M3 - 文章

AN - SCOPUS:79952443544

SN - 0165-0114

VL - 171

SP - 93

EP - 105

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 1

ER -

Graphical L₂-stability analysis of Takagi-Sugeno control systems in the frequency domain

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Keywords

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