Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

Anbalagan, Pratap; Raja, R.; Alzabut, Jehad; Dianavinnarasi, J.; Cao, Jinde; Rajchakit, Grienggrai

doi:10.1007/s11063-019-10154-1

Cited by 96 publications

(42 citation statements)

References 47 publications

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“…Recently, several activation functions been considered to study the QVNNs [32,33,38,40]. There are two different approaches that have been well regarded among them.…”

Section: Resultsmentioning

confidence: 99%

“…There are two different approaches that have been well regarded among them. The first approach is that the activation functions are not expressed directly by dividing real and imaginary parts [33], and the second approach is that the function of activation can be expressed by dividing real and imaginary parts [40]. Accordingly, the main results of this paper will be derived by using the real-imaginary separate type activation function.…”

Section: Resultsmentioning

confidence: 99%

“…It is easy to know that the use of free-weighting parameters υ p (p = 1, ...12) can reduce the conservativeness of theoretical results. Thus, compared with that in [37,38,40], our approach is more effective and feasible.…”

Section: Theoremmentioning

confidence: 96%

“…In addition, fractional-order derivatives have many advantages compared to integer order calculus in defining an infinite memory and inherited properties [36]. Therefore, 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]. To the best of our knowledge, the current results of this paper have not yet been proposed for FOQVMNNs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

et al. 2020

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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.

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“…Recently, several activation functions been considered to study the QVNNs [32,33,38,40]. There are two different approaches that have been well regarded among them.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

et al. 2020

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“…It has a tremendous potential to be utilized in synapsis for simulation of the human brain by replacing a resistor with a memristor [4][5][6]. In view of these characteristics, a new neural network (NN) model, namely, the memristive neural network (MNN) has been widely studied, and many theoretical papers regarding various dynamics of MNNs have been published in recent years [7][8][9][10][11][12][13]. From the real-world application perspective, time delays inherently arise in many practical systems including NNs.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

et al. 2020

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In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

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Exponential Input‐To‐State Stability of Quaternion‐Valued Memristive Neural Networks: Continuous and Discrete Cases

Li,

Cao,

Abdel‐Aty

2024

Adaptive Control & Signal

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This article focuses on the input‐to‐state stability (ISS) issue of quaternion‐valued memristive networks. Employing the quaternion norm tool and the Lyapunov method, two improved conclusions are developed for the continuous networks. After that, via the semidiscretization technique, a new discrete model is designed, and its ISS performance is discussed and subsequently recur to a nonlinear scalarization approach. Less conservative results are obtained since the nonlinear scalarization approach makes the quaternion interval meaningful. Simulations are presented to verify the validity of the outcomes.

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Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

Cited by 96 publications

References 47 publications

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

Exponential Input‐To‐State Stability of Quaternion‐Valued Memristive Neural Networks: Continuous and Discrete Cases

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