Exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.     

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.     

变时滞BAM神经网络的全局指数稳定性

研究一类变时滞BAM神经网络平衡点的全局指数稳定性问题.在不要求激励函数全局Lipschitz条件下,通过构造合适的Lyapunov泛函,并结合Young不等式,得到了BAM神经网络模型在一定条件下全局指数稳定的一些充分条件,推广和改进了前人的相关结论,为综合设计指数稳定的时滞BAM神经网络提供了依据.     

Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms

This paper is concerned with global asymptotic stability of a class of reaction-diffusion stochastic Bi-directional Associative Memory (BAM) neural networks with discrete and distributed delays. Based on suitable assumptions, we apply the linear matrix inequality (LMI) method to propose some new sufficient stability conditions for reaction-diffusion stochastic BAM neural networks with discrete and distributed delays. The obtained results are easy to check and improve upon the existing stability results. An example is also given to demonstrate the effectiveness of the obtained results.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.     

Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses

An impulsive Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with distributed delays is studied. Some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self regulation functions. The approaches are based on Laypunov–Kravsovskii functional and homeomorphism theory. When our results are applied to the BAM neural networks, our results generalize some previously known results. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg-type bidirectional associative memory networks.     

Some criteria for robust stability of Cohen–Grossberg neural networks with delays

This paper considers the problem of robust stability of Cohen–Grossberg neural networks with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Comparisons between our results and previous results admits our results establish a new set of stability criteria for delayed Cohen–Grossberg neural networks. Numerical examples are given to illustrate the effectiveness of our results.     

Neural networks with discrete and distributed time-varying delays: A general stability analysis

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with both the discrete and distributed time-varying delays. By using appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. Therefore, the stability of the neural networks can be checked readily by resorting to the Matlab LMI toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the discrete and distributed time-varying delays, which means that our results generalize and further improve those in the earlier publications. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions.     

Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays

In this paper, global exponential stability is studied for a class of high-order bidirectional associative memory (BAM) neural networks with time-varying delays. An approach combining the Lyapunov functional with the Linear Matrix Inequality (LMI) is taken to study the problems. Several sufficient conditions are presented for ensuring the system to be globally exponentially stable. Three typical examples are presented to show the application of the criteria obtained in this paper.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Global dissipativity of a class of BAM neural networks with time-varying and unbound delays

In this paper, we study the global dissipativity of a class of BAM neural networks with both time-varying and unbound delays. Based on Lyapunov functions and inequality techniques, several algebraic criteria for the global dissipativity are obtained. And the linear matrix inequality (LMI) approach is exploited to establish sufficient easy-to-test conditions which are related to the derivative of delay for the global dissipativity. Meanwhile, the estimations of the positive invariant set, globally attractive set and globally exponential attractive set are given out. Finally, two examples are presented and analyzed to demonstrate our results.     

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.     

Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays

In this paper, a class of impulsive Cohen-Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the homeomorphism theory, the M-matrix theory and inequality technique, some new general sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen-Grossberg-type BAM neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulsive disturbed intension. An example is given to show the effectiveness of the results obtained here.     

Exponential convergence rate estimation for uncertain delayed neural networks of neutral type

The global exponential stability for a class of uncertain delayed neural networks (DNNs) of neutral type is investigated in this paper. Delay-dependent and delay-independent criteria are proposed to guarantee the robust stability of DNNs via LMI and Razumikhin-like approaches. For a given delay, the maximal allowable exponential convergence rate will be estimated. Some numerical examples are given to illustrate the effectiveness of our results. The simulation results reveal significant improvement over the recent results.     

左Clifford拟正则半群的半直积和圈积

在半群不含单位元的情况下,给出了两个半群的半直积和圈积是左Clifford拟正则半群的充分必要条件.     

具有时滞的扩散BAM神经网络的指数稳定性

研究一类具有反应扩散的滞后BAM神经网络平衡点的存在性唯一性和全局指数稳定性.运用拓扑同胚映射,Lyapunov泛函以及多参数方法,得到关于平衡点存在唯一性和全局指数稳定性的充分条件,将相关文献的结果推广到正整数r范数上.     

Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: An LMI approach

In this paper, we consider the stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. By utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, some sufficient LMI-based conditions are obtained to guarantee the global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. These conditions can be easily checked via the MATLAB LMI toolbox. Moreover, the obtained results extend and improve the earlier publications. Finally, a numerical example is provided to demonstrate the low conservatism and effectiveness of the proposed LMI conditions.     

NEW CRITERIA OF EXPONENTIAL STABILITY FOR BAM NEURAL NETWORKS WITH DELAYS

In this Letter,a novel Lyapunov functional is constructed to investigate the exponential stability of the BAM neural networks.New sufficient conditions of the uniqueness and global exponential stability for the equilibrium of BAM neural networks with delays are obtained.The results improve those existing ones.     

Exponential convergence estimates for neural networks with discrete and distributed delays

In this paper, the problems of determining the global exponential stability and estimating the exponential convergence rate are investigated for a class of neural networks with mixed discrete and distributed time-varying delays. By employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is exploited to establish sufficient easy-to-test conditions for the neural networks to be globally exponentially stable, which can be readily solved by using the numerically efficient Matlab LMI toolbox. Three numerical examples are provided to demonstrate the effectiveness of the proposed results.