TY - JOUR
T1 - Fractional-order discontinuous systems with indefinite LKFs
T2 - An application to fractional-order neural networks with time delays
AU - Udhayakumar, K.
AU - Rihan, Fathalla A.
AU - Rakkiyappan, R.
AU - Cao, Jinde
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2022/1
Y1 - 2022/1
N2 - 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.
AB - 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.
KW - Discontinuous activations
KW - Fixed-time synchronization
KW - Fractional-order
KW - Lyapunov-Krasovskii functional
KW - Signed neural networks
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U2 - 10.1016/j.neunet.2021.10.027
DO - 10.1016/j.neunet.2021.10.027
M3 - Article
C2 - 34798343
AN - SCOPUS:85119068612
SN - 0893-6080
VL - 145
SP - 319
EP - 330
JO - Neural Networks
JF - Neural Networks
ER -