# Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

**Remark**

**1.**

**Lemma**

**1**

**.**For given matrix $Z\in {\mathbb{R}}^{n},Z>0$, scalars ${\tau}_{2}>{\tau}_{1}$, vector function $w:\left[{\tau}_{1},{\tau}_{2}\right]\in {R}^{n}$, the following inequality holds

## 3. Main Results

#### 3.1. Construction of the Lyapunov Function

**Theorem**

**1.**

**Proof.**

#### 3.2. Introduction of Fuzzy Framework

**Remark**

**2.**

**Remark**

**3.**

**Remark**

**4.**

#### 3.3. Design of Sampled-Data Controller

**Theorem**

**2.**

**Proof.**

## 4. Numerical Examples

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Technologies | Maximum Sampling Internal |
---|---|

T-set | 0.583 |

Pareto optimality under T-set | 0.624 |

Intuitionistic fuzzy T-set | 0.652 |

Proposed method | 0.681 |

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**MDPI and ACS Style**

Zheng, M.; Su, Y.; Yan, C.
Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models. *Symmetry* **2024**, *16*, 108.
https://doi.org/10.3390/sym16010108

**AMA Style**

Zheng M, Su Y, Yan C.
Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models. *Symmetry*. 2024; 16(1):108.
https://doi.org/10.3390/sym16010108

**Chicago/Turabian Style**

Zheng, Minjie, Yulai Su, and Changjian Yan.
2024. "Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models" *Symmetry* 16, no. 1: 108.
https://doi.org/10.3390/sym16010108