Further results on stability analysis of Takagi–Sugeno fuzzy time-delay systems via improved Lyapunov–Krasovskii functional

Rupak Datta; Ramasamy Saravanakumar; Rajeeb Dey; Baby Bhattacharya; Rupak Datta; Ramasamy Saravanakumar; Rajeeb Dey; Baby Bhattacharya

doi:10.3934/math.2022901

AIMS Mathematics

2022, Volume 7, Issue 9: 16464-16481. doi: 10.3934/math.2022901

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Research article

Further results on stability analysis of Takagi–Sugeno fuzzy time-delay systems via improved Lyapunov–Krasovskii functional

1.
Department of Mathematics, National Institute of Technology Agartala, Tripura 799046, India
2.
Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan
3.
Department of Electrical Engineering, National Institute of Technology Silchar, Assam 788010, India

Received: 25 April 2022 Revised: 26 June 2022 Accepted: 03 July 2022 Published: 07 July 2022
MSC : 34D20, 34E05

The problem of delay-range-dependent (DRD) stability analysis for continuous time Takagi–Sugeno (T–S) fuzzy time-delay systems (TDSs) is addressed in this paper. An improved DRD stability criterion is proposed in an linear matrix inequality (LMI) framework by constructing an appropriate delay-product-type (DPT) Lyapunov–Krasovskii functional (LKF) to make use of Bessel-Legendre polynomial based relaxed integral inequality. The modification in the proposed LKF along with the judicious choice of integral inequalities helps to obtain a less conservative delay upper bound for a given lower bound. The efficacy of the obtained stability conditions is validated through the solution of three numerical examples.
- T–S fuzzy system,
- LKF,
- DRD stability,
- LMI,
- TDS
Citation: Rupak Datta, Ramasamy Saravanakumar, Rajeeb Dey, Baby Bhattacharya. Further results on stability analysis of Takagi–Sugeno fuzzy time-delay systems via improved Lyapunov–Krasovskii functional[J]. AIMS Mathematics, 2022, 7(9): 16464-16481. doi: 10.3934/math.2022901

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Abstract

The problem of delay-range-dependent (DRD) stability analysis for continuous time Takagi–Sugeno (T–S) fuzzy time-delay systems (TDSs) is addressed in this paper. An improved DRD stability criterion is proposed in an linear matrix inequality (LMI) framework by constructing an appropriate delay-product-type (DPT) Lyapunov–Krasovskii functional (LKF) to make use of Bessel-Legendre polynomial based relaxed integral inequality. The modification in the proposed LKF along with the judicious choice of integral inequalities helps to obtain a less conservative delay upper bound for a given lower bound. The efficacy of the obtained stability conditions is validated through the solution of three numerical examples.

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