Improved results on synchronization in arrays of coupled delayed neural networks with hybrid coupling

In order to investigate the influence of hybrid coupling on the synchronization of delayed neural networks, by choosing an improved delay-dependent Lyapunov-Krasovskii functional, one less conservative asymptotical criterion based on linear matrix inequality （LMI） is established. The Kronecker product and convex combination techniques are employed. Also the bounds of time-varying delays and delay derivatives are fully considered. By adjusting the inner coupling matrix parameters and using the Matlab LMI toolbox, the design and applications of addressed coupled networks can be realized. Finally, the efficiency and applicability of the proposed results are illustrated by a numerical example with simulations.

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.

Global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.

Nonlinear H_∞ control of structured uncertain stochastic neural networks with discrete and distributed time varying delays

This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the existence of H∞ control based on the Lyapunov stability theory. The stability criterion is described in terms of linear matrix inequalities （LMIs）, which can be easily checked in practice. An example is provided to demonstrate the effectiveness of the proposed result.

Stability for Cellular Neural Networks with Delay

The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.

Robust fuzzy control of Takagi-Sugeno fuzzy neural networks with discontinuous activation functions and time delays

The problem of global robust asymptotical stability for a class of Takagi-Sugeno fuzzy neural networks（TSFNN） with discontinuous activation functions and time delays is investigated by using Lyapunov stability theory.Based on linear matrix inequalities（LMIs）,we originally propose robust fuzzy control to guarantee the global robust asymptotical stability of TSFNNs.Compared with the existing literature,this paper removes the assumptions on the neuron activations such as Lipschitz conditions,bounded,monotonic increasing property or the right-limit value is bigger than the left one at the discontinuous point.Thus,the results are more general and wider.Finally,two numerical examples are given to show the effectiveness of the proposed stability results.

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks （DNNs） with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality （LMI） are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control al- gorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.

Stability analysis of delayed cellular neural networks with and without noise perturbation

The stability of a class of delayed cellular neural networks （DCNN） with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.

Stability and Stabilization on Generalized Delay Stochastic Neural Network with Distributed Parameter

Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito differential formula to the constructed average function with respect to spatial variables along the system considered under the integral operator. Some sufficient conditions are given.

Almost sure exponential stability of neutral stochastic delayed cellular neural networks

In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

Stability of discrete Hopfield neural networks with delay

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network＇s applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.

Exponential Stability for Delayed Cellular Neural Networks

The exponential stability of the delayed cellular neural networks （DCNN＇s） is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Liapunov function. It is shown that the conditions differ from previous ones. The new conditions, which are associated with some initial value, are represented by some blocks of the interconnection matrix.

Exponential stability for cellular neural networks: an LMI approach

A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.

Stability and attractive basins of multiple equilibria in delayed two-neuron networks

Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation flmctions of 2r （r 〉 1） corner points is studied. Sufficient conditions are established for checking the existence of （2r ＋ 1）2 equilibria in delayed recurrent neural networks. Under these conditions, （r ＋ 1）2 equilibria are locally exponentially stable, and （2r＋ 1）2 -（r ＋ 1）2 -r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.

Time delay recursive neural network-based direct adaptive control for a piezo-actuated stage

Piezo-actuated stage is a core component in micro-nano manufacturing field.However,the inherent nonlinearity,such as rate-dependent hysteresis,in the piezo-actuated stage severely impacts its tracking accuracy.This study proposes a direct adaptive control(DAC)method to realize high precision tracking.The proposed controller is designed by a time delay recursive neural network.Compared with those existing DAC methods designed under the general Lipschitz condition,the proposed control method can be easily generalized to the actual systems,which have hysteresis behavior.Then,a hopfield neural network(HNN)estimator is proposed to adjust the parameters of the proposed controller online.Meanwhile,a modular model consisting of linear submodel,hysteresis submodel,and lumped uncertainties is established based on the HNN estimator to describe the piezoactuated stage in this study.Thus,the performance of the HNN estimator can be exhibited visually through the modeling results.The proposed control method eradicates the adverse effects on the control performance arising from the inaccuracy in establishing the offline model and improves the capability to suppress the influence of hysteresis on the tracking accuracy of piezo-actuated stage in comparison with the conventional DAC methods.The stability of the control system is studied.Finally,a series of comparison experiments with a dual neural networks-based data driven adaptive controller are carried out to demonstrate the superiority of the proposed controller.

Discrete-time delayed standard neural network model and its application

A novel neural network model, termed the discrete-time delayed standard neural network model （DDSNNM）, and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks （RNNs） and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed （or non-delayed） nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks （CNNs） and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.

LOCAL STABILITY AND BIFURCATION IN A THREE-UNIT DELAYED NEURAL NETWORK

A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.

Wind Power Forecasting Using Wavelet Transforms and Neural Networks with Tapped Delay

With an objective to improve wind power estimation accuracy and reliability,this paper presents Linear Neural Networks with Tapped Delay(LNNTD)in combination with wavelet transform(WT)for probabilistic wind power forecasting in a time series framework.For comparison purposes,results of the proposed model are compared with the benchmark model,different neural networks and WT based models considering performance indices such as accuracy,execution time and R^(2) statistic.For the reliability and proper validation of the proposed model,this paper highlights the probabilistic forecast attributes at different skill tests.The historical data of the Ontario Electricity Market(OEM)for the period 2011–2014 were used and tested for two years from November 2012 to October 2014 with one month moving window considering all seasonal aspects.The experimental results clearly show that the results of the proposed model have been found to be better than others.