Stability analysis for nonlinear fractional-order systems based on comparison principle
详细信息 查看全文
- 作者：Zhiliang Wang (1)
Dongsheng Yang (1)
Tiedong Ma (2)
Ning Sun (3) - 关键词：Nonlinear fractional ; order system ; Caputo derivative ; Chaos ; Synchronization ; Comparison principle
- 刊名：Nonlinear Dynamics
- 出版年：2014
- 出版时间：January 2014
- 年：2014
- 卷：75
- 期：1-2
- 页码：387-402
- 全文大小：
- 作者单位：Zhiliang Wang (1)
Dongsheng Yang (1)
Tiedong Ma (2)
Ning Sun (3)
1. School of Information Science and Engineering, Northeastern University, Shenyang, 110819, P.R. China
2. College of Automation, Chongqing University, Chongqing, 400044, P.R. China
3. Jilin Electric Power Co. Ltd., Changchun, 130021, Jilin Province, P.R. China - ISSN：1573-269X
文摘
This work constructs a theoretical framework for the stability analysis of nonlinear fractional-order systems. A new definition, the generalized Caputo fractional derivative, is proposed for the first time. Based on that, the comparison principles for scalar and vector fractional-order systems are constructed, respectively. Furthermore, a sufficient theorem for stability analysis is proved, and how to use this theorem in stabilization is also discussed. Three examples have been presented to illustrate how to use the developed theory to analyze the stability and to design stabilization controllers. With the proposed method, the problems of stabilization and synchronization of the fractional-order chaotic fractional-order systems can be easily solved with linear feedback control.