﻿ 分数阶混沌系统有限时间稳定性分析及同步控制 Analysis of Finite-Time Stability of Fractional-Order Chaotic System and Its Synchronization Control

Pure Mathematics
Vol.07 No.03(2017), Article ID:20533,8 pages
10.12677/PM.2017.73022

Analysis of Finite-Time Stability of Fractional-Order Chaotic System and Its Synchronization Control

Dandan Liu, Caixia Gao

Institute of Mathematical Science, Inner Mongolia University, Hohhot Inner Mongolia

Received: Apr. 29th, 2017; accepted: May 13th, 2017; published: May 17th, 2017

ABSTRACT

In this paper, the finite time stability and synchronization control of fractional order chaotic systems are studied; based on the Lyapunov fractional stability theory, the determination method of finite time stability for a class of nonlinear fractional chaotic systems is proposed, and it’s more generic than the existing results. And the synchronous controller is designed by the method; in the case of all the variables are met in the system, the different structure of the driver system and the response system are synchronized. Numerical simulation results demonstrate the effectiveness of the proposed method.

Keywords:Fractional-Order Chaotic System, Finite-Time Stability, Synchronization Control

1. 引言

2. 分数阶微积分

(1)

Caputo分数阶微分定义为

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

3. 主要结果

3.1. 有限时间稳定性分析

(1)

(2)

(3)

(11)

(12)

(13)

，由条件1可知，代入(13)式可得

(1) 满足定理1的条件(1)，(2)，

(2)

3.2. 同步控制器设计

(14)

(15)

(16)

(17)

4. 数值仿真

(a)(b)

Figure 1. Fractional order chaotic Liu system

(a) (b)

Figure 2. Fractional order chaotic Lorenz system

Figure 3. The curve of control inputs

Figure 4. The curve of synchronization error

5. 结论

Analysis of Finite-Time Stability of Fractional-Order Chaotic System and Its Synchronization Control[J]. 理论数学, 2017, 07(03): 168-175. http://dx.doi.org/10.12677/PM.2017.73022

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