New Result on Mismatched Double Fuzzy Summation Inequality

Feng Li; Zhenghao Ni; Sangmoon Lee; Hao Shen

doi:10.1109/TFUZZ.2025.3554757

New Result on Mismatched Double Fuzzy Summation Inequality

Feng Li
, Zhenghao Ni
, Sangmoon Lee
, Hao Shen

Anhui University of Technology
Kyungpook National University

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

4 Scopus citations

Abstract

This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.

Original language	English
Pages (from-to)	2376-2381
Number of pages	6
Journal	IEEE Transactions on Fuzzy Systems
Volume	33
Issue number	7
DOIs	https://doi.org/10.1109/TFUZZ.2025.3554757
State	Published - 2025

Keywords

Imperfect premise matching
mismatched double fuzzy summation inequality Takagi–Sugeno (TS) fuzzy systems
mismatched membership function

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10.1109/TFUZZ.2025.3554757

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title = "New Result on Mismatched Double Fuzzy Summation Inequality",

abstract = "This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.",

keywords = "Imperfect premise matching, mismatched double fuzzy summation inequality Takagi–Sugeno (TS) fuzzy systems, mismatched membership function",

author = "Feng Li and Zhenghao Ni and Sangmoon Lee and Hao Shen",

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T1 - New Result on Mismatched Double Fuzzy Summation Inequality

AU - Li, Feng

AU - Ni, Zhenghao

AU - Lee, Sangmoon

AU - Shen, Hao

PY - 2025

Y1 - 2025

N2 - This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.

AB - This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.

KW - Imperfect premise matching

KW - mismatched double fuzzy summation inequality Takagi–Sugeno (TS) fuzzy systems

KW - mismatched membership function

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M3 - Article

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SP - 2376

EP - 2381

JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

IS - 7

ER -

New Result on Mismatched Double Fuzzy Summation Inequality

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Keywords

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