# Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

^{1}

^{2}

^{*}

## Abstract

**:**

^{1}positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz nonlinear systems.

## 1. Introduction

## 2. Preliminary Results

#### 2.1. Finite-Time Stability

**Definition**

**1.**

**Definition**

**2.**

**Theorem**

**1.**

- $V(x)$ is positive definite on $\tilde{U},$ and
- $\dot{V}(x)+c\phantom{\rule{3.33333pt}{0ex}}{V}^{\alpha}(x)\u2a7d0$, $\forall x\in \tilde{U}$.

#### 2.2. Finite-Time Stabilizing Feedback

**Theorem**

**2.**

**Lemma**

**1.**

**Lemma**

**2.**

**Lemma**

**3.**

**Lemma**

**4.**

**Lemma**

**5.**

## 3. Proof of Theorem 2

**Proposition**

**1.**

**Proposition**

**2.**

**Proof.**

**Proposition**

**3.**

**Proof.**

## 4. Simulations of the Controller

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Khelil, N.; Otis, M.J.-D. Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems. *Mathematics* **2016**, *4*, 58.
https://doi.org/10.3390/math4040058

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Khelil N, Otis MJ-D. Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems. *Mathematics*. 2016; 4(4):58.
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**Chicago/Turabian Style**

Khelil, Nawel, and Martin J.-D. Otis. 2016. "Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems" *Mathematics* 4, no. 4: 58.
https://doi.org/10.3390/math4040058