Novel delay dependent stability analysis of Takagi—Sugeno fuzzy uncertain neural networks with time varying delays

This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi-Sugeno (T-S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.     

New results on stability criteria for neural networks with time-varying delays

In this paper,the problem of stability analysis for neural networks with time-varying delays is considered.By constructing a new augmented Lyapunov-Krasovskii’s functional and some novel analysis techniques,improved delaydependent criteria for checking the stability of the neural networks are established.The proposed criteria are presented in terms of linear matrix inequalities(LMIs) which can be easily solved and checked by various convex optimization algorithms.Two numerical examples are included to show the superiority of our results.     

Dynamics of Cohen-Grossberg neural networks with variable and distributed delays

This paper is concerned with the analysis problem for the exponential stability of a class of Cohen-Grossberg neural networks with variable and distributed delays. Some sufficient conditions ensuring the existence, uniqueness and exponential stability of the equilibrium point are obtained by employing Brouwer’s fixed-point theorem and by applying the inequality technique. In the results, we do not assume that the activation function satisfies the boundedness and the Lipschitz condition. Three numerical examples are given to show the effectiveness of the obtained results.     

Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays

This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).     

Robust stability analysis of Takagi-Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

In this paper,the global stability of Takagi-Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered.A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs.The proposed stability conditions are demonstrated through numerical examples.Furthermore,the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed.Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.     

Chaotification for a class of cellular neural networks with distributed delays

In this Letter, the chaotification for a class of cellular neural networks with distributed delays is studied. On the basis of the largest Lyapunov exponent, the sensitivity to the initial conditions is studied for the distributed delays with kernel being weak and strong. Some theoretical results about the chaotification for the neural network with distributed time delays are derived. Finally, two numerical simulations are presented to illustrate the effectiveness of the theoretical results.     

Global exponential stability of reaction diffusion neural networks with discrete and distributed time-varying delays

This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays.By constructing a more general type of Lyapunov-Krasovskii functional combined with a free-weighting matrix approach and analysis techniques,delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities.The obtained results are dependent on the size of the time-varying delays and the measure of the space,which are usually less conservative than delay-independent and space-independent ones.These results are easy to check,and improve upon the existing stability results.Some remarks are given to show the advantages of the obtained results over the previous results.A numerical example has been presented to show the usefulness of the derived linear matrix inequality(LMI)-based stability conditions.     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

时滞双向联想记忆神经网络的全局稳定性

通过构造一个合适的Lyapunov泛函及应用不等式的分析技巧研究了具有时滞的双向联想记忆 神经网络的平衡点的全局稳定性问题-在对神经元激励函数较宽松的假设条件下（可以不满 足Lipschitz条件），获得了一个新的保证全局渐近稳定性的判定准则-结果可应用于包含非 Lipschitz的一类更加广泛的神经元激励函数的神经网络的设计中- 关键词： Lyapunov泛函 时滞 双向联想记忆神经网络 全局渐近稳定性     

Finite-time synchronization of memristor-based complex-valued neural networks with time delays

This paper deals with the problem of finite-time synchronization of memristor-based complex-valued neural networks (MCVNNs) with time delays. Based on the theory of differential inclusions with discontinuous right-hand side, we establish a new algebraic criterion of the finite-time synchronization of memristor-based complex-valued neural networks with time delays. The obtained theoretical results complement and improve some existing achievements in the real number field. Meanwhile, the obtained sufficient condition is conducive to qualitative analysis for some complex-valued nonlinear delayed systems. In the end, the conclusion is substantiated with an example of numerical simulation.     

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's functional and use of Finsler's lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Global asymptotic stability of fuzzy cellular neural networks with time-varying delays

In this Letter fuzzy cellular neural networks with time-varying delays are studied. Sufficient conditions for the existence, uniqueness and global asymptotic stability of equilibrium point are established by using the theory of topological degree and applying the properties of nonsingular M-matrix. The activation functions are not required to be differentiable, bounded or monotone nondecreasing. The results of this Letter are new and they complement previously known results.     

Stability analysis of Markovian jumping stochastic Cohen Grossberg neural networks with discrete and distributed time varying delays

In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays （MJSCGNNs） is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Dynamical analysis of Cohen–Grossberg neural networks with distributed delays

In this Letter, a model describing dynamics of Cohen–Grossberg neural networks with distributed delays is considered. Without assuming Lipschitz conditions on activation functions, by employing Brouwer's fixed point theorem and applying inequality technique, some new sufficient conditions on the existence, uniqueness and exponential stability of equilibrium point are obtained. Finally, two examples with their numerical simulations are provided to show the correctness of our analysis.     

Global exponential robust stability of reaction–diffusion interval neural networks with time-varying delays

The authors discuss the existence of the equilibrium point and its global exponential robust stability for reaction–diffusion interval neural networks with time-varying delays by means of the topological degree theory and Lyapunov-functional method. Since the diffusion phenomena, time delay and the perturbation due to noises as well as some unforced man-made faults could not be ignored in neural networks, the model presented here is close to the actual systems, and the sufficient conditions on global exponential robust stability established in this Letter, which are easily verifiable, have a wider adaptive range.     

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.     

Analysis on global exponential robust stability of reaction-diffusion neural networks with S-type distributed delays

To avoid the unstable phenomena caused by time delays and perturbations, we investigate the sufficient conditions to ensure the global exponential robust stability with a convergence rate for the reaction-diffusion neural networks with S-type distributed delays. Because S-type distributed delays lead to some difficulty, we also introduce a new generalized Halanay inequality and a novel method-system-approximation method into the qualitative research of neural networks. Moreover, the sufficient criteria provided here, which are rather accessible and feasible, have wider adaptive range.     

Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties

This Letter deals with the problem of exponential stability for a class of delayed Hopfield neural networks. Based on augmented parameter-dependent Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stability are obtained for two cases of time-varying delays: the delays are differentiable and have an upper bound of the delay-derivatives, and the delays are bounded but not necessary to be differentiable. The conditions are presented in terms of linear matrix inequalities, which allow to compute simultaneously two bounds that characterize the exponential stability rate of the solution. Numerical examples are included to illustrate the effectiveness of our results.     

Novel criteria of synchronization stability in complex networks with coupling delays

Complex networks are wide spread in the real world, arising in fields as disparate as sociology, physics and biology. The information spreading through a complex network is often associated with time delays due to the finite speeds of signal transmission over a distance. Hence, complex networks with coupling delays have gained increasing attention in various fields of science and engineering today. In this paper, based on the theory of asymptotic stability of linear time-delay systems, synchronization stability in complex dynamical networks with coupling delays is investigated, and we derive novel criteria of synchronization state for both delay-independent and delay-dependent stabilities. As illustrative examples, we use the networks with coupling delays and a given coupling scheme to test the theoretical results.     

State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.