A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks. (March 2020)

• Record Type: Journal Article
• Authors: Chen, Chuan; Li, Lixiang; Peng, Haipeng; Yang, Yixian; Mi, Ling; Zhao, Hui
• Is Part Of: Neural networks. Volume 123(2020)
• Page Start: 412
• Page End: 419
• Publication Date: 2020-03
• Subjects: Fixed-time stability -- Fixed-time synchronization -- Neural networks; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2019.12.028
• Languages: English
• ISSNs: 0893-6080

Abstract

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.