Abstract
This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.
Highlights
Memristor is regarded as the fourth basic circuit element, which was first proposed by Chua [1].In 2008, the first practical memristor device was invented by the HP company [2]
In order to analyze QVNNs a suitable approach is to divide the QVNN into two complex-valued neural networks (CVNNs) or four real-valued neural networks (RVNNs) systems based on the non-commutative quaternion multiplication
This paper offers a better approach for studying the stability of FOQVMNNs
Summary
Memristor is regarded as the fourth basic circuit element, which was first proposed by Chua [1]. In [26], based on the non-commutativity of quaternion multiplication, global exponential stability for QVNNs was analyzed by separating QVNNs into four RVNNs. In [27], leakage delay-dependent synchronization conditions for fractional-order QVNNs with discrete delays have been studied. The problem of global Mittag–Leffler stability and synchronization for fractional-order QVNNs was studied in [31]. The use of fractional-order calculus in NN models could describe better dynamic behavior, and many excellent results on fractional-order NNs have been published, such as the problem of global robust synchronization, Mittag–Leffler synchronization, quasi-pinning synchronization, and finite-time Mittag–Leffler stability [37,38,39,40]. RVNNs. By use of the homeomorphism principle, Lyapunov fractional-order derivative, set-valued maps, and some analytical methods, new sufficient conditions for global Mittag–Leffler stability and stabilization of FOQVMNNs are derived.
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