Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses

In this paper, the robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses is considered. It is assumed that the considered impulsive neural networks have norm-bounded parametric uncertainties and time-varying delays and the state variables on the impulses may relate to the time-varying delays. By using Lyapunov functions together with Razumikhin technique or with differential inequalities, some new robust exponential stability criteria are provided. Some examples and their simulations, including examples that the stability of which can not be tackled by the existing results, are also presented to illustrate the effectiveness and the advantage of the obtained results.     

New results on passivity analysis of uncertain neural networks with time-varying delays

In this paper, the passivity problem is investigated for a class of uncertain neural networks with generalized activation functions. By employing an appropriate Lyapunov–Krasovskii functional, a new delay-dependent criterion for the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. An example is given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.     

Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays

This paper investigates the global asymptotic stability problem for a class of neutral-type complex-valued neural networks with random time-varying delays. By introducing a stochastic variable with Bernoulli distribution, the information of time-varying delay is assumed to be random time-varying delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing inequality technique, several sufficient conditions are obtained to ensure the global asymptotically stability of equilibrium point for the considered neural networks. The obtained stability criterion is expressed in terms of complex-valued linear matrix inequalities, which can be simply solved by effective YALMIP toolbox in MATLAB. Finally, three numerical examples are given to demonstrate the efficiency of the proposed main results.     

Finite-time stability of neutral-type neural networks with random time-varying delays

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov–Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.     

Dissipativity and periodic attractor for non-autonomous neural networks with time-varying delays

In this paper, a model is considered to describe the dynamics of a class of non-autonomous neural networks with time-varying delays. By applying the properties of M-matrix, the techniques of inequality analysis and the Banach fixed point theorem, we obtain a series of new criteria on the dissipativity and existence of periodic attractor. Our results can extend and improve earlier ones.     

Dissipativity and passivity analysis of Markovian jump impulsive neural networks with time delays

This paper discusses the issue of dissipativity and passivity analysis for a class of impulsive neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modelled as a continuous-time discrete-state Markov chain. Based on a multiple integral inequality technique, a novel delay-dependent dissipativity criterion is established via a suitable Lyapunov functional involving the multiple integral terms. The proposed dissipativity and passivity conditions for the impulsive neural networks are represented by means of linear matrix inequalities. Finally, three numerical examples are given to show the effectiveness of the proposed criteria.     

变时滞神经网络指数同步性的LMI新条件

研究了一类具有变时滞的非线性混沌神经网络的指数同步性问题。应用线性矩阵不等式和Lyapunov泛函方法,得到了具有驱动-响应结构的神经网络的指数同步性准则,建立了判断神经网络同步性的新的充分条件。通过实例说明了该方法的可行性和有效性。     

Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components

In this paper, the problem of stability criteria of neural networks with two additive time-varying delay components is investigated. Some new delay-dependent stability criteria are derived in terms of linear matrix inequalities by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because reciprocally convex approach and convex polyhedron approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

This paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.     

Exponential stability analysis of stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed delays

In this paper, we study a new class of stochastic Cohen-Grossberg neural networks with reaction-diffusion and mixed delays. Without the aid of nonnegative semimartingale convergence theorem, the method of variation parameter and linear matrix inequalities technique, a set of novel sufficient conditions on the exponential stability for the considered system is obtained by utilizing a new Lyapunov-Krasovskii functional, the Poincaré inequality and stochastic analysis theory. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Therefore, our results generalize and improve some earlier publications. Moreover, two numerical examples are given to show the effectiveness of the theoretical results and demonstrate that the stability criteria existed in the earlier literature fail.     

Global exponential stability for neutral-type BAM neural networks with time-varying delays

In this article, the global exponential stability of neutral-type bidirectional associative memory (BAM) neural networks with time-varying delays is analysed by utilizing the Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach. New sufficient conditions ensuring the global exponential stability of neutral-type BAM neural networks is obtained by using the powerful MATLAB LMI control toolbox. In addition, an example is provided to illustrate the applicability of the result.     

Passivity analysis for neural networks with a time-varying delay

This paper deals with the problem of passivity analysis for neural networks with both time-varying delay and norm-bounded parameter uncertainties by employing an improved free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov-Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, for two types of time-varying delays, less conservative delay-dependent passivity conditions are obtained in terms of linear matrix inequalities (LMIs), respectively. Finally, a numerical example is given to demonstrate the effectiveness of the proposed techniques.     

带加性时变时滞的不确定神经网络鲁棒散耗性研究

针对加性时变时滞不确定神经网络的时滞相关鲁棒耗散性问题,提出了一种更一般化的激活函数。与以往研究不同,充分考虑了关于神经元激活函数和加性时变时滞的充分信息,通过使用一些新的积分项构造合适的Lyapunov-Krasovskii泛函（LKF）,并利用新生成的单积分不等式来计算其导数,包括延森不等式和维特林积分不等式的特殊情形。利用线性矩阵不等式（LMI）技术建立了一个新的时滞相关的不守恒全局渐近稳定性和耗散准则。最终通过计算和数值仿真验证了所提理论的有效性。     

Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays

This paper investigates the event-triggered state estimation problem of Markovian jumping impulsive neural networks with interval time-varying delays. The purpose is to design a state estimator to estimate system states through available output measurements. In the neural networks, there are a set of modes, which are determined by Markov chain. A Markovian jumping time-delay impulsive neural networks model is employed to describe the event-triggered scheme and the network- related behaviour, such as transmission delay, data package dropout and disorder. The proposed event-triggered scheme is used to determine whether the sampled state information should be transmitted. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. First, we design a state observer to estimate the neuron states. Second, based on a novel Lyapunov-Krasovskii functional (LKF) with triple-integral terms and using an improved inequality, several sufficient conditions are derived. The derived conditions are formulated in terms of a set of linear matrix inequalities , under which the estimation error system is globally asymptotically stable in the mean square sense. Finally, numerical examples are given to show the effectiveness and superiority of the results.     

pth moment stability analysis of stochastic recurrent neural networks with time-varying delays

This paper addresses, in great detail, the issue of pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. With the help of the Dini-derivative of the expectation of V(t,X(t)) “along” the solution X(t) of the model and the technique of Halanay-type inequality, some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established. Results of the development as presented in this paper are more general than those reported in some previously published papers. An example is also given to illustrate that our results are correct and effectiveness.     

Novel passivity criteria for neural networks with discrete and unbounded distributed time-varying delays

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria.     

时滞Hopfield神经网络的随机稳定性分析

T-S模型提供了一种通过模糊集和模糊推理将复杂的非线性系统表示为线性子模型的方法。研究了时滞Hopfield神经网络的随机稳定性（SFVDHNNs）。首先描述了SFVDHNNs模型,然后用Lyapunov方法研究了SFVDHNNs全局均方指数稳定性,通过可以被一些标准的数值分析方法求解的线性矩阵不等式（LMIs）得出了稳定性标准。     

Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for uncertain stochastic fuzzy interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs), which can be solved by some standard numerical packages. Finally, numerical examples are given to show the effectiveness and merits of the proposed method.     

Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays

In this paper, a class of stochastic impulsive high-order BAM neural networks with time-varying delays is considered. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order BAM neural networks.