Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales

By employing time scale calculus theory, free weighting matrix method and linear matrix inequality (LMI) approach, several delay-dependent sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the neural networks with both infinite distributed delays and general activation functions on time scales. Both continuous-time and discrete-time neural networks are described under the same framework by the reported method. Illustrated numerical examples are given to show the effectiveness of the theoretical analysis. It is noteworthy that the activation functions are assumed to be neither bounded nor monotone.     

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.     

Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions

This paper investigates the global asymptotic stability of the periodic solution for a general class of neural networks whose neuron activation functions are modeled by discontinuous functions with linear growth property. By using Leray-Schauder alternative theorem, the existence of the periodic solution is proved. Based on the matrix theory and generalized Lyapunov approach, a sufficient condition which ensures the global asymptotical stability of a unique periodic solution is presented. The obtained results can be applied to check the global asymptotical stability of discontinuous neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also conform the validity of Forti’s conjecture for discontinuous neural networks with linear growth activation functions. Two illustrative examples are given to demonstrate the effectiveness of the present results.     

Global exponential stability analysis of delayed Cohen--Grossberg neural networks with distributed delays

In this article, the global exponential stability problem of Cohen--Grossberg neural networks with both discrete-time delays and distributed delays is investigated. The existence and global stability for the unique equilibrium of the Cohen--Grossberg neural networks with distributed delays are achieved by using some new Lyapunov functionals, M-matrix theory and some analytic techniques, and some less restrictive conditions are obtained. An example is also worked out to validate the advantages of our results.     

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

In this paper, the global robust stability is investigated for interval neural networks with multiple time-varying delays. The neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Without assuming both the boundedness on the activation functions and the differentiability on the time-varying delays, a new sufficient condition is presented to ensure the existence, uniqueness, and global robust stability of equilibria for interval neural networks with multiple time-varying delays based on the Lyapunov–Razumikhin technique as well as matrix inequality analysis. Several previous results are improved and generalized, and an example is given to show the effectiveness of the obtained results.     

Relaxed delay-dependent exponential stability condition for a class of neural networks with polytopic uncertainties and distributed delays

The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.     

一类变时滞神经网络的全局指数稳定性

在不要求激活函数有界的前提下,利用Lyapunov泛函方法和线性矩阵不等式(LMI)分析技巧,研究了一类变时滞神经网络平衡点的存在性和全局指数稳定性.给出判别网络全局指数稳定性的判据,推广了现有文献中的一些结果.这些判据具有LMI的形式,进而易于验证.仿真例子表明了所得结果的有效性.     

中立联想记忆神经网络鲁棒稳定性新准则

针对一类具有离散时滞和参数范数有界的不确定性中立联想记忆神经网络的全局渐近鲁棒稳定性问题进行了研究.通过应用范数理论和矩阵不等式分析方法,并构造合适的Lyapunov-Krasovskii泛函,推导出了与时滞无关的新稳定性判定准则,用于保证神经网络的平衡点是全局渐近鲁棒稳定的.该准则中包含的未知参数少、计算复杂度低,易于验证.仿真算例验证了新判定准则的有效性.     

Global exponential stability in Lagrange sense for periodic neural networks with various activation functions

In this paper, global exponential stability in Lagrange sense for periodic neural networks with various activation functions is further studied. By constructing appropriate Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of periodic neural networks. These theoretical analysis can narrow the search field of optimization computation, associative memories, chaos control and provide convenience for applications.     

New results concerning the exponential stability of delayed neural networks with impulses

Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here.     

On delayed uncertain genetic regulatory networks: robust stability analysis

In this paper, the problem of stability analysis for uncertain genetic regulatory networks with time-varying delays is investigated. The time-varying delay function in this paper is not required to be either continuously differentiable, or its derivative less than one. By choosing an appropriate Lyapunov–Krasovskii functional and employing some free-weighting matrices, some new delay-dependent and delay-derivative-dependent stability criteria are presented in terms of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Finally, three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.     

Global stability analysis in Cohen-Grossberg neural networks with delays and inverse Hölder neuron activation functions

In this paper, a novel class of Cohen-Grossberg neural networks with delays and inverse Hölder neuron activation functions are presented. By using the topological degree theory and linear matrix inequality (LMI) technique, the existence and uniqueness of equilibrium point for such Cohen-Grossberg neural networks is investigated. By constructing appropriate Lyapunov function, a sufficient condition which ensures the global exponential stability of the equilibrium point is established. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks

This paper is concerned with the problem of finite-time stability analysis for uncertain stochastic delayed reaction-diffusion genetic regulatory networks. The parameter uncertainties are assumed to be norm-bounded, and the time delays are assumed to be time-varying. Based on the Lyapunov functional method, sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. When there are no norm-bounded parameter uncertainties in the networks, a finite-time stochastic stability condition is also established. All the conditions are diffusion-dependent as well as delay-dependent. Numerical examples are given to illustrate the effectiveness of the proposed results.     

Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect

This paper investigates the problem of the dynamical behaviours of a class of complex-valued neural networks with mixed time delays and impulsive effect. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for assuring the exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and mathematical induction method. The obtained results generalise the existing ones. Finally, two numerical examples with simulations are given to demonstrate the feasibility of the proposed results.     

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.     

Robust stability of delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales

In this paper, the global robust exponential stability of equilibrium solution to delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is studied. Using topological degree theory, M-matrix method, Lyapunov functional and inequality skills, we establish some sufficient conditions for the existence, uniqueness and global robust exponential stability of equilibrium solution to delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales. One example is given to illustrate the effectiveness of our results.     

时延细胞神经网络的全局渐近稳定性

通过构造新的Lyapunov泛函,在Lyapunov泛函中巧妙引入可调的实参数,并结合不等式运用的一些技巧,讨论了时延细胞神经网络的全局渐近稳定性问题,得到了该模型的平衡点全局渐近稳定的一些新的充分条件。所得的结果改进推广了已有文献中相应的一些结论,并且可应用于以前所不能处理的若干情形。理论分析和数学推导表明,全局渐近稳定性的一个简单充分判据与时延是有关的。所得结果突出了时延对于细胞神经网络的全局渐近稳定性的影响,这对于设计带时延的细胞神经网络有着重要的参考价值。此外,通过实例说明了相应结果的应用,这在理论上和应用中都有着重要的意义。     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

New results on robust exponential stability for discrete recurrent neural networks with time-varying delays

This paper is concerned with the problem of robust exponential stability analysis for uncertain discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, some novel stability conditions are proposed via a new Lyapunov function. Neither any model transformation nor free-weighting matrices are employed in our theoretical derivation. The established stability criteria significantly improve and simplify some existing stability conditions. Numerical examples are given to demonstrate the effectiveness of the proposed methods.