Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays

K. Udhayakumar, Fathalla A. Rihan, R. Rakkiyappan, Jinde Cao

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this article, we discuss bipartite fixed-time synchronization for fractional-order signed neural networks with discontinuous activation patterns. The Filippov multi-map is used to convert the fixed-time stability of the fractional-order general solution into the zero solution of the fractional-order differential inclusions. On the Caputo fractional-order derivative, Lyapunov-Krasovskii functional is proved to possess the indefinite fractional derivatives for fixed-time stability of fragmentary discontinuous systems. Furthermore, the fixed-time stability of the fractional-order discontinuous system is achieved as well as an estimate of the new settling time. The discontinuous controller is designed for the delayed fractional-order discontinuous signed neural networks with antagonistic interactions and new conditions for permanent fixed-time synchronization of these networks with antagonistic interactions are also provided, as well as the settling time for permanent fixed-time synchronization. Two numerical simulation results are presented to demonstrate the effectiveness of the main results

Original languageEnglish
Pages (from-to)319-330
Number of pages12
JournalNeural Networks
Volume145
DOIs
Publication statusPublished - Jan 2022

Keywords

  • Discontinuous activations
  • Fixed-time synchronization
  • Fractional-order
  • Lyapunov-Krasovskii functional
  • Signed neural networks

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence

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