Finite-time stabilization of discontinuous fuzzy inertial Cohen–Grossberg neural networks with mixed time-varying delays

This article aims to study a class of discontinuous fuzzy inertial Cohen–Grossberg neural networks (DFICGNNs) with discrete and distributed time-delays. First of all, in order to deal with the discontinuities by the differential inclusion theory, based on a generalized variable transformation including two tunable variables, the mixed time-varying delayed DFICGNN is transformed into a first-order differential system. Then, by constructing a modified Lyapunov–Krasovskii functional concerning with the mixed time-varying delays and designing a delayed feedback control law, delay-dependent criteria formulated by algebraic inequalities are derived for guaranteeing the finite-time stabilization (FTS) for the addressed system. Moreover, the settling time is estimated. Some related stability results on inertial neural networks is extended. Finally, two numerical examples are carried out to verify the effectiveness of the established results

Finite-time stabilization for fractional-order inertial neural networks with time varying delays

This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results

Finite time Synchronization of Inertial Memristive Neural Networks with Time Varying Delay

Finite time synchronization control of inertial memristor-based neural networks with varying delay is considered. In view of drive and response concept, the sufficient conditions to ensure finite time synchronization issue of inertial memristive neural networks is given. Based on Lyapunov finite time asymptotic theory, a kind of feedback controllers is designed for inertial memristorbased neural networks to realize the finite time synchronization. Based on Lyapunov stability theory, close loop error system can be proved finite time and fixed time stable. Finally, illustrative example is given to illustrate the effectiveness of theoretical results

Global Mittag-Leffler stability of Caputo fractional-order fuzzy inertial neural networks with delay

This paper deals with the global Mittag-Leffler stability (GMLS) of Caputo fractional-order fuzzy inertial neural networks with time delay (CFOFINND). Based on Lyapunov stability theory and global fractional Halanay inequalities, the existence of unique equilibrium point and GMLS of CFOFINND have been established. A numerical example is given to illustrate the effectiveness of our results

Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations

pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales

In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time domain by applying feedback control. We formulate the problem by using the time scales theory so that the results can be applied to any uniform or non-uniform time domains. Also, we provide a comparison of results that shows that obtained results are unified and generalize the existing results. Mainly, we use the unified matrix-measure theory and Halanay inequality to establish these results. In the last section, we provide two simulated examples for different time domains to show the effectiveness and generality of the obtained analytical results.Comment: 20 pages, 18 figure

New results of global Mittag-Leffler synchronization on Caputo fuzzy delayed inertial neural networks

This article is devoted to discussing the problem of global Mittag-Leffler synchronization (GMLS) for the Caputo-type fractional-order fuzzy delayed inertial neural networks (FOFINNs). First of all, both inertial and fuzzy terms are taken into account in the system. For the sake of reducing the influence caused by the inertia term, the order reduction is achieved by the measure of variable substitution. The introduction of fuzzy terms can evade fuzziness or uncertainty as much as possible. Subsequently, a nonlinear delayed controller is designed to achieve GMLS. Utilizing the inequality techniques, Lyapunov’s direct method for functions and Razumikhin theorem, the criteria for interpreting the GMLS of FOFINNs are established. Particularly, two inferences are presented in two special cases. Additionally, the availability of the acquired results are further confirmed by simulations