Abstract
In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.
Highlights
Bidirectional associative memory (BAM) neural networks are a type of extended unidirectional auto-associator of Hopfield neural networks. ey are composed of two layers: the X-layer and the Y-layer, which can store and recall pattern pairs [1]
Motivated by the above discussion, we investigate the global Mittag–Leffler stability of fractional-order BAM neural networks with linear feedback controllers, including single and whole state feedback controllers. e main contributions include the following: First, a novel lemma is proposed using basic inequality to broaden the choice of the Lyapunov function
Linear state feedback control is designed to induce the stability of fractional-order BAM neural networks, including a single linear state feedback control and the whole linear state feedback control
Summary
Bidirectional associative memory (BAM) neural networks are a type of extended unidirectional auto-associator of Hopfield neural networks. ey are composed of two layers: the X-layer and the Y-layer, which can store and recall pattern pairs [1]. In [15], the global Mittag–Leffler stability of multiple equilibrium points for the impulsive fractional-order quaternionvalued neural networks is investigated by employing the Lyapunov method. E finite-time Mittag–Leffler stability for fractional-order quaternion-valued memristive neural networks with impulsive effect is investigated in [20]. With linear and partial state feedback controls, global Mittag–Leffler stability of fractional-order BAM neural network is analyzed using Caputo fractional derivative and generalized Gronwall inequality [27]. Motivated by the above discussion, we investigate the global Mittag–Leffler stability of fractional-order BAM neural networks with linear feedback controllers, including single and whole state feedback controllers. Ird, some sufficient conditions for global Mittag–Leffler stability are given by using the fractional Lyapunov method and introducing feedback controllers.
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