Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays

The robust asymptotic stability analysis for uncertain BAM neural networks with both interval time-varying delays and stochastic disturbances is considered. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges for delays, some new stability criteria are established to guarantee the delayed BAM neural networks to be robustly asymptotically stable in the mean square. Unlike the most existing mean square stability conditions for BAM neural networks, the supplementary requirements that the time derivatives of time-varying delays must be smaller than 1 are released and the lower bounds of time varying delays are not restricted to be 0. Furthermore, in the proposed scheme, the stability conditions are delay-range-dependent and rate-dependent/independent. As a result, the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples are given to illustrate the effectiveness of the proposed criteria.     

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.     

The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

The global asymptotic stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms is investigated. Under some suitable assumptions and using Lyapunov–Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.     

Relaxed stability conditions for delayed recurrent neural networks with polytopic uncertainties

This paper investigates the problem of stability analysis for recurrent neural networks with time-varying delays and polytopic uncertainties. Parameter-dependent Lypaunov functionals are employed to obtain sufficient conditions that guarantee the robust global exponential stability of the equilibrium point of the considered neural network. The derived stability criteria are expressed in terms of a set of relaxed linear matrix inequalities, which can be easily tested by using commercially available software. Two numerical examples are provided to demonstrate the effectiveness of the proposed results.     

Robust exponential stabilization of a class of delayed neural networks with reaction-diffusion terms

In this paper, the problem of global robust exponential stabilization for a class of neural networks with reaction-diffusion terms and time-varying delays which covers the Hopfield neural networks and cellular neural networks is investigated. A feedback control gain matrix is derived to achieve the global robust exponential stabilization of the neural networks by using the Lyapunov stability theory, and the stabilization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Finally, a numerical simulation illustrates the effectiveness of the results.     

Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations

In this paper, by using the Lyapunov method, Itô’s differential formula and linear matrix inequality (LMI) approach, the global robust power-rate stability in mean square is discussed for genetic regulatory networks with unbounded time-varying delay, noise perturbations and parameter uncertainties. Sufficient conditions are given to ensure the robust power-rate stability (in mean square) of the genetic regulatory networks. Meanwhile, the criteria ensuring global power-rate stability in mean square are a byproduct of the criteria guaranteeing global robust power-rate stability in mean square. The obtained conditions are derived in terms of linear matrix inequalities (LMIs) which are easy to be verified via the LMI toolbox. An illustrative example is given to show the effectiveness of the obtained result.     

变时延神经网络的全局指数稳定性及收敛性

利用Lyapunov泛函方法和线性矩阵不等式（LMI）技术,通过引入一系列参数,给出全局指数稳定的平衡点的判别条件和时延的最大上界和神经网络的收敛速度,所得结果较之一些文献中的结果简单、实用并且对于具体设计带时延神经网络有重要的指导意义.最后,通过实例表明给出的判定条件是有效、可行的.     

具有混合时滞和脉冲效应的随机反应扩散Cohen-Grossberg神经网络的指数稳定性

研究了一类具有混合时滞和脉冲效应的随机反应扩散Cohen—Grossberg神经网络模型,应用M-矩阵,It微分公式和分析技巧,得到了模型平衡点的全局均方指数稳定性的充分条件,所得结果推广了已有的工作．     

Attractability and location of equilibrium point of cellular neural networks with time-varying delays

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.     

一类具变时滞的模糊BAM神经网络的平衡点的指数稳定性(英文)

研究一类具变时滞的模糊BAM神经网络.利用拓扑度论和微分不等式,获得了该类网络平衡点的存在性、唯一性和全局指数稳定性的充分条件.一个例子用来解释本文获得的结果.     

Robust stability of stochastic delayed genetic regulatory networks

Gene regulation is an intrinsically noisy process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations. In this paper, we consider the robust stability analysis problem of genetic regulatory networks with time-varying delays and stochastic perturbation. Different from other papers, the genetic regulate system considers not only stochastic perturbation but also parameter disturbances, it is in close proximity to the real gene regulation process than determinate model. Based on the Lyapunov functional theory, sufficient conditions are given to ensure the stability of the genetic regulatory networks. All the stability conditions are given in terms of LMIs which are easy to be verified. Illustrative examples are presented to show the effectiveness of the obtained results.     

Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.     

多比例时滞细胞神经网络的指数周期性与稳定性

研究了一类具多比例时滞细胞神经网络的全局指数周期性与稳定性.通过变换y(t)=x(e~t)将具多比例时滞的细胞神经网络变换成具常时滞变系数的细胞神经网络,利用一些分析技巧与构造合适的Lyapunov泛函,得到系统的周期解存在唯一且全局指数周期的时滞依赖的充分条件,判断方法简单易验证.并给出了两个例子及其数值仿真结果以支持所得结论.     

New criteria of almost periodic solution for bam neural networks with delays and impulsive effects

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.     

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen–Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen–Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.     

Robust exponential stability of markovian jumping neural networks with time-varying delay

This paper considers the robust stability of a class of neural networks with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov-Krasovskii functional, a sufficient condition for the global exponential stability of the delayed Markovian jumping neural networks is established. The proposed condition is also extended to the uncertain cases, which are shown to be the improvement and extension of the existing ones. Finally, the validity of the results are illustrated by an example.     

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.     

变时滞区间细胞神经网络的全局鲁棒稳定性

利用拓扑度理论和Liapunov泛函方法讨论了变时滞区间细胞神经网络的全局鲁棒稳定性．给出了实用有效的判定条件,推广了有关文献中的结果．