A new system of global fractional-order interval implicit projection neural networks

Abstract

The purpose of this paper is to introduce and investigate a new system of global fractional-order interval implicit projection neural networks. An existence and uniqueness theorem of the equilibrium point for the system of global fractional-order interval implicit projection neural networks is obtained under some suitable assumptions. Moreover, Mittag-Leffler stability for the system of global fractional-order interval implicit projection neural networks is also proved. Finally, two numerical examples are given to illustrate the validity of our results.

Global Mittag-Leffler stability of Fractional-Order Projection Neural Networks with Impulses

“…Remark 4.1. In [24,25], authors studied stability of fractional-order projection neural networks without impulse. Unlike the previous results, we have considered the stability of projection neural networks with impulsive effects by utilizing the general quadratic Lyapunov function.…”

“…It is well known that, the projection neural network (dynamical system), captured the desired features of both the variational inequality and the dynamical systems within the same framework, can be used to solve many constrained optimization problems, variational inequality problems, equilibrium point problems, dynamic traffic networks and so on (see, for example, [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and the references therein). Taking into account of the advantages of fractional calculus, Wu and Zou [24], for the first time, proposed a class of fractional order projective dynamical systems.…”

“…Taking into account of the advantages of fractional calculus, Wu and Zou [24], for the first time, proposed a class of fractional order projective dynamical systems. Wu et al [25] proposed a new system of global fractionalorder interval implicit projection neural networks and showed Mittag-Leffler stability of the equilibrium point for such fractional-order projection neural networks under suitable conditions. On the basic of the linear matrix inequality technique, Li et al [29] obtained some sufficient conditions to ensure the asymptotical stability of the equilibrium point of the addressed projection neural networks.…”

Output feedback passification of a class of fractional-order static neural networks

“…Many important and interesting problems on fractional-order neural networks (FONNs) such as Lyapunov stability (Yang et al, 2018; Yao et al, 2020; Zhang et al, 2017), finite-time stability (Yang et al, 2021; Wu et al, 2015), passivity analysis (Ding et al, 2019; Padmaja and Balasubramaniam, 2021; Sau et al, 2020; Thuan et al, 2020), synchronization (Wang et al, 2019a), state estimation (Nagamani et al, 2020), guaranteed cost control (Thuan and Huong, 2019), and H ∞ control problems (Sau et al, 2021; Thuan et al, 2020) have been studied by many authors. Note that almost all research investigation concentrated on the fractional-order local field NNs (Ding et al, 2019; Nagamani et al, 2020; Padmaja and Balasubramaniam, 2021; Sau et al, 2020; Thuan and Huong, 2019; Thuan et al, 2020; Wang et al, 2019a; Wu et al, 2015; Yang et al, 2018; Zhang et al, 2017), while relatively few of them concentrated on the fractional-order static neural networks (FOSNNs) (Wu et al, 2016a, 2016b, 2018; Wu and Zou, 2014; Yao et al, 2020; Yang et al, 2021).…”

A new class of global fractional-order projective dynamical system with an application

“…We note that IVP (4) is presented in the most abstract form and also covers many important problems in projective dynamical system, variational inequality and fractional differential equation as special cases [11][12][13]16,[32][33][34][35][36][37]39,40,42,[45][46][47]. If M is a linear map, g (x(t)) = x(t), r = 0 and N = 0, then IVP (4) reduces to the general form of (1).…”