title: Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks.
abstract: In this paper, the fixed-time stability of dynamical systems and the fixed-time synchronization of coupled discontinuous neural networks are investigated under the framework of Filippov solution. Firstly, by means of reduction to absurdity, a theorem of fixed-time stability is established and a high-precision estimation of the settling-time is given. It is shown by theoretic proof that the estimation bound of the settling time given in this paper is less conservative and more accurate compared with the classical results. Besides, as an important application, the fixed-time synchronization of coupled neural networks with discontinuous activation functions is proposed. By designing a discontinuous control law and using the theory of differential inclusions, some new criteria are derived to ensure the fixed-time synchronization of the addressed coupled networks. Finally, two numerical examples are provided to show the effectiveness and validity of the theoretical results.
authors.affiliation: College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046 Xinjiang, China. Electronic address: wacheng2003@163.com.
authors.forename: Cheng
authors.initials: C
authors.lastname: Hu
authors.affiliation: College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046 Xinjiang, China.
authors.forename: Juan
authors.initials: J
authors.lastname: Yu
authors.affiliation: College of Mathematics and Statistics, Yili Normal University, Yining, 835000 Xinjiang, China.
authors.forename: Zhanheng
authors.initials: Z
authors.lastname: Chen
authors.affiliation: College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046 Xinjiang, China.
authors.forename: Haijun
authors.initials: H
authors.lastname: Jiang
authors.affiliation: Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar. Electronic address: tingwen.huang@qatar.tamu.edu.
authors.forename: Tingwen
authors.initials: T
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Discontinuous neural network; Dynamical system; Fixed-time stability; Fixed-time synchronization