Finite-time Stability of Fractional-order Complex-valued Neural Networks with Time Delays

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

“…In [33,34,44], the authors have focused on studying the finite-time stability of fractional-order delayed neural networks. However, it should be pointed out that the finite-time stability and asymptotic stability in the sense of Lyapunov are different concepts, because finite-time stability does not contain Lyapunov asymptotic stability and vice versa [34,47]. This is also the motivation of this paper.…”

“…For example, Song and Cao [26] have established some sufficient conditions to 2 Complexity ensure the existence and uniqueness of the nontrivial solution by using the contraction mapping principle, Krasnoselskii fixed point theorem, and the inequality technique, in which uniform stability conditions of fractional-order neural networks are also derived in fixed time-intervals. Note that timedelay (see [23][24][25][31][32][33][34][35][36][37]) is a common phenomenon and is inevitable in practice, which often exists in almost every neural network and has an important effect on the stability and performance of system.…”

“…For example, Mittag-Leffler stability of fractional-order delayed neural networks has been investigated by applying fractional Lyapunov direct method [28,30,32]. The finite-time stability of Caputo fractional-order delayed neural networks has been studied by applying Gronwall's inequality approach and inequality scaling techniques [33,34]. The delay-independent stability criteria of Riemann-Liouville fractional-order neutral-type delayed neural networks have been proposed based on classical Lyapunov functional method [35].…”

“…In [46], globally asymptotic stability problem of impulsive fractional-order neural networks with discrete delays has been studied, yet the existence of the equilibrium solution for fractional-order BAM neural networks has not been taken into account. On the other hand, it should be pointed out that the finite-time stability and asymptotic stability in the sense of Lyapunov are different concepts, because finite-time stability does not contain Lyapunov asymptotic stability and vice versa [34,47]. Although the signal transmission is sometimes instantaneous modelling with discrete delays, it may be sometimes a distribution propagation delay over a period of time so that distributed delays (see [20,23,25]) should not be ignored in the model.…”

Robust guaranteed cost control for time‐delay fractional‐order neural networks systems

“…By employing linear delay feedback control and a fractional‐order inequality, the problems of synchronization of a class of fractional‐order complex‐valued neural networks with time delay were considered in the work of Bao et al Bao et al established several sufficient criteria to make sure that the fractional‐order coupled delayed neural networks is synchronized by means of the fractional‐order Lyapunov stability theorem. The problem of finite‐time stability for FONNs systems with or without time delays was considered in other works . Very recently, Song et al investigated the mixed H ∞ and passive projective synchronization problem for fractional‐order memristor‐based neural networks with time delay.…”