Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with
K Udhayakumar1, Fathalla A Rihan2, R Rakkiyappan3
1Department of Mathematics, Bharathiar University, Coimbatore 641 046, India; Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain, 15551, United Arab Emirates.
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.
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