A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date: Jan 7, 2020

Abstract

In this paper, we derive a new fixed-time stability theorem based on definite integral, variable substitution and some inequality techniques. The fixed-time stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, the fixed-time synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixed-time synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixed-time synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixed-time stability theorems. Moreover, the plaintext signals can be recovered according to the new fixed-time stability theorem, while the plaintext signals cannot be recovered according to the existing fixed-time stability theorems.

Authors

  • Chuan Chen
    Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.
  • Lixiang Li
    Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.
  • Haipeng Peng
    Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.
  • Yixian Yang
    Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.
  • Ling Mi
    School of Mathematics and Statistics, Qilu University of Technology, Jinan 250353, China. Electronic address: miling@lyu.edu.cn.
  • Hui Zhao
    School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong, 723000, Shaanxi, China.

Keywords

External Resources

Popular Topics
Recent Journals