Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays

This paper is concerned with the robust delay-dependent exponential stability of uncertain stochastic neural networks (SNNs) with mixed delays. Based on a novel Lyapunov-Krasovskii functional method, some new delay-dependent stability conditions are presented in terms of linear matrix inequalities, which guarantee the uncertain stochastic neural networks with mixed delays to be robustly exponentially stable. Numerical examples are given to illustrate the effectiveness of our results.     

Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters

In this paper, we investigate the robust exponential stability for stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jump parameters. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain sufficient conditions for the exponential stability of the equilibrium solution. The obtained stability criteria can be easily checked by linear matrix inequality (LMI) techniques. Finally numerical examples are provided to illustrate the obtained theoretical result.     

Further results for global exponential stability of stochastic memristor-based neural networks with time-varying delays

In recent years, the stability problems of memristor-based neural networks have been studied extensively. This paper not only takes the unavoidable noise into consideration but also investigates the global exponential stability of stochastic memristor-based neural networks with time-varying delays. The obtained criteria are essentially new and complement previously known ones, which can be easily validated with the parameters of system itself. In addition, the study of the nonlinear dynamics for the addressed neural networks may be helpful in qualitative analysis for general stochastic systems. Finally, two numerical examples are provided to substantiate our results.     

Robust stability of uncertain Markovian jump discrete-time recurrent neural networks with time delays

This article is concerned with robust stochastic stability for a class of uncertain Markovian jump discrete-time recurrent neural networks (MJDRNNs) with time delays. The uncertainty is assumed to be of the norm-bounded form. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, some sufficient criteria are proposed for the robust stochastic stability in the mean square of the MJDRNNs with constant or mode-dependent time delays. The proposed LMI-based results are computationally efficient as they can be solved numerically using standard commercial software. The validity of the obtained results are further illustrated by two simulation examples.     

Further results on delay-dependent stability criteria of neural networks with time-varying delays.

In this brief paper, an augmented Lyapunov functional, which takes an integral term of state vector into account, is introduced. Owing to the functional, an improved delay-dependent asymptotic stability criterion for delayed neural networks (NNs) is derived in term of linear matrix inequalities (LMIs). It is shown that the obtained criterion can provide less conservative result than some existing ones. When linear fractional uncertainties appear in NNs, a new robust delay-dependent stability condition is also given. Numerical examples are given to demonstrate the applicability of the proposed approach.     

Stability of stochastic Markovian jump neural networks with mode-dependent delays

In this paper, the problem of stability analysis for a general class of uncertain stochastic neural networks with Markovian jumping parameters and mixed mode-dependent delays is considered. By the use of a new Markovian switching Lyapunov–Krasovskii functional, delay-dependent conditions on mean square asymptotic stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.     

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

This paper focuses on the problem of delay-dependent robust stability analysis for a class of uncertain stochastic neural networks with time-varying delay by employing improved free-weighting matrix method. Taking the relationship among the time-varying delay, its upper bound and their difference into account and using It[^(o)]'s\hbox{It}\hat{o}\hbox{'s} differential formula, some improved LMI-based delay-dependent stability criteria for stochastic neural networks are obtained without ignoring any terms, which guarantee systems globally robustly stochastically stable in the mean square. Finally, three numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

Moment exponential stability analysis of Markovian jump stochastic differential equations with uncertain transition jump rates

This paper is concerned with the moment exponential stability analysis of Markovian jump stochastic differential equations. The equations under consideration are more general, whose transition jump rates matrix Q is not precisely known. Sufficient conditions for testing the stability of such equations are established, and some numerical examples to illustrate the effectiveness of our results are presented.     

New delay-dependent exponential stability criteria of BAM neural networks with time delays

In this paper, the global exponential stability is investigated for the bi-directional associative memory networks with time delays. Several new sufficient conditions are presented to ensure global exponential stability of delayed bi-directional associative memory neural networks based on the Lyapunov functional method as well as linear matrix inequality technique. To the best of our knowledge, few reports about such “linearization” approach to exponential stability analysis for delayed neural network models have been presented in literature. The method, called parameterized first-order model transformation, is used to transform neural networks. The obtained conditions show to be less conservative and restrictive than that reported in the literature. Two numerical simulations are also given to illustrate the efficiency of our result.     

New delay-dependent exponential stability criteria for neural networks with discrete and distributed time-varying delays

In this paper, the problem of exponential stability criteria for neural networks with discrete and distributed time-varying delays are considered. By dividing the discrete delay interval into multiple segments and choosing a new class of Lyapunov functional which contains tripe-integral terms, some new delay-dependent stability criteria are derived in terms of linear matrix inequalities. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Global exponential stability for uncertain delayed neural networks of neutral type with mixed time delays.

The global exponential stability for a class of uncertain delayed neural networks (DNNs) of neutral type with mixed delays is investigated in this paper. Delay-dependent and delay-independent stability criteria are proposed to guarantee the robust stability and uniqueness of equilibrium point of DNNs via linear matrix inequality and Razumikhin-like approaches. Two classes of perturbations on weighting matrices are considered in this paper. Some numerical examples are illustrated to show the effectiveness of our results.     

New delay-dependent stability criteria for cohen-grossberg neural networks with multiple time-varying mixed delays

This paper investigates the globally asymptotical stability problem for a general class of Cohen-Grossberg neural networks with multiple mixed time-delays. Before proving the main theorem, a more generalized convex combination inequality is proposed. A new stability criterion for Cohen-Grossberg neural networks with multiple time-varying delays is obtained by the employed general inequality technique. Two examples are included to illustrate the effectiveness of the presented results.     

Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays.

This correspondence provides stochastic exponential stability for Markovian jumping bidirectional associative memory neural networks with time-varying delays. An approach combining the Lyapunov functional with linear matrix inequality is taken to study the problems. Some criteria for the stochastic exponential stability are derived. The results obtained in this correspondence are less conservative, less restrictive, and more computationally efficient than the ones reported so far in the literature.     

Robust stability of Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent delays

This article discusses the robust stability problem for a class of uncertain Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent time delays. The transition probabilities of the mode jumps are considered to be partly unknown, which relax the traditional assumption in Markovian jump systems that all of them must be completely known a priori. The mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jump modes. By employing the Lyapunov functional and linear matrix inequality approach, some sufficient criteria are derived for the robust stability of the underlying systems. A numerical example is exploited to illustrate the developed theory.     

模型相关时变时滞马尔可夫跳变系统低保守稳定性

本文研究了时变时滞与模型相关的随机马尔可夫跳变系统的时滞相关稳定性问题. 通过建立时变时滞与模型相关的系统模型, 构造不同的Lyapunov-Krasovskii函数, 并通过引入改进的积分等式, 以线性矩阵不等式的形式提出了具有较小保守性的时滞依赖稳定性条件. 最后用几个数值算例说明本文结论的有效性及较低的保守性.     

不确定随机离散分布时滞神经网络的鲁棒稳定性*

采用Its微分公式和不等式分析技巧,研究了一类不确定随机离散分布时滞神经网络的鲁棒稳定性问题。该模型同时考虑了神经网络模型的两种扰动因素,即随机扰动与不确定性扰动。通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了系统在均方根意义下的全局鲁棒稳定性判据,能够利用LMI工具箱很容易地进行检验。此外,仿真结果进一步证明了结论的有效性。     

Novel delay-dependent stability condition for mixed delayed stochastic neural networks with leakage delay signals

In this paper, the problem of stability condition for mixed delayed stochastic neural networks with neutral delay and leakage delay is investigated. A novel Lyapunov functional is constructed with double and triple integral terms. New sufficient conditions are derived to guarantee the global asymptotic stability of the concerned neural network. This paper is more general than the paper by Zhu et al. [Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms, Neural Process. Lett. 41 (2015), pp. 1–27]. In our paper, we considered both the neutral delay and leakage delay, but the paper by Zhu et al. is not considering the neutral delay. Also we employed triple integrals in the Lyapunov functional which is not used in the paper by Zhu et al. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.     

Delay-dependent exponential stability for uncertain neutral stochastic neural networks with interval time-varying delay

This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov–Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results.     

Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays

In this letter, the global asymptotical stability analysis problem is considered for a class of Markovian jumping stochastic Cohen-Grossberg neural networks (CGNNs) with mixed delays including discrete delays and distributed delays. An alternative delay-dependent stability analysis result is established based on the linear matrix inequality (LMI) technique, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Neither system transformation nor free-weight matrix via Newton-Leibniz formula is required. Two numerical examples are included to show the effectiveness of the result.