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.     

Further results on delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays and Markovian jump parameters

This paper studies the problem of the robustly exponential stability of uncertain stochastic neural networks with mixed delays and Markovian jump parameters. In terms of linear matrix inequalities approach, some new delay-dependent stability criteria are established for the considered systems by constructing a modified Lyapunov–Krasovskii functional. And our derived results shown by three illustrative examples are more effective than some existing ones.

     

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

Stability of uncertain impulsive stochastic fuzzy neural networks with two additive time delays in the leakage term

This paper is concerned with the stability problem for a class of impulsive neural networks model, which includes simultaneously parameter uncertainties, stochastic disturbances and two additive time-varying delays in the leakage term. By constructing a suitable Lyapunov–Krasovskii functional that uses the information on the lower and upper bound of the delay sufficiently, a delay-dependent stability criterion is derived by using the free-weighting matrices method for such Takagi–Sugeno fuzzy uncertain impulsive stochastic recurrent neural networks. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasibility can be checked easily by MATLAB LMI Control toolbox. Finally, the theoretical result is validated by simulations.     

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.     

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.     

Exponential synchronization of stochastic chaotic neural networks with mixed time delays and Markovian switching

This paper studies the exponential synchronization problem for a class of stochastic perturbed chaotic neural networks with both Markovian jump parameters and mixed time delays. The mixed delays consist of discrete and distributed time-varying delays. At first, based on a Halanay-type inequality for stochastic differential equations, by virtue of drive-response concept and time-delay feedback control techniques, a delay-dependent sufficient condition is proposed to guarantee the exponential synchronization of two identical Markovian jumping chaotic-delayed neural networks with stochastic perturbation. Then, by utilizing the Jensen integral inequality and a novel Lemma, another delay-dependent criterion is established to achieve the globally stochastic robust synchronization. With some parameters being fixed in advance, these conditions can be solved numerically by employing the Matlab software. Finally, a numerical example with their simulations is provided to illustrate the effectiveness of the presented synchronization scheme.     

Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The 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. By constructing a Lyapunov–Krasovskii functional, and using poincarè inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.     

Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays

The problem of delay-dependent stability analysis is investigated for discrete-time Markovian jump neural networks with mixed time-delays (both discrete and infinity-distributed time delays). The Markov chain in the underlying neural networks is finite piecewise homogeneous. A delay-dependent condition is derived for the addressed neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same type of neural networks but with partially known transition probabilities. Two numerical examples are given to demonstrate the usefulness of the derived methods.     

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.     

Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching

This paper presents new stability results for recurrent neural networks with Markovian switching. First, algebraic criteria for the almost sure exponential stability of recurrent neural networks with Markovian switching and without time delays are derived. The results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration. Next, both delay-dependent and delay-independent criteria for the almost sure exponential stability of recurrent neural networks with time-varying delays and Markovian-switching parameters are derived by means of a generalized stochastic Halanay inequality. The results herein include existing ones for recurrent neural networks without Markovian switching as special cases. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay

In this paper, robust control of uncertain stochastic recurrent neural networks with time-varying delay is considered. A novel control method is given by using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several delay-independent and delay-dependent sufficient conditions are then further derived to ensure the global asymptotical stability in mean square for the uncertain stochastic recurrent neural networks, and the estimation gains can also be obtained. Numerical examples are constructed to verify the theoretical analysis in this paper.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Improved Delay-Dependent Asymptotic Stability Criteria for Delayed Neural Networks

This brief is concerned with asymptotic stability of neural networks with uncertain delays. Two types of uncertain delays are considered: one is constant while the other is time varying. The discretized Lyapunov–Krasovskii functional (LKF) 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 asymptotic stability of delayed neural networks (DNNs). A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing stability criteria.      

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.     

New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays

This letter considers the robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. By using Lyapunov–Krasovskii functional and Itô’s differential formula, several new sufficient conditions guaranteeing the global robust exponential stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and less conservativeness of our results.     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

一类含有时变时滞的不确定中立型Hopfield神经网络的鲁棒稳定性判据

针对一类不确定中立型时变时滞Hopfield神经网络的鲁棒稳定性问题, 构造了一个新Lyapunov-Krasovskii泛函, 并结合自由矩阵方法和牛顿—莱布尼茨公式, 得到了新的时滞相关稳定性判据. 该判据考虑了中立型时变时滞Hopfield神经网络中的参数不确定性, 所得结果以线性矩阵不等式(Linear matrix inequality, LMI)的形式给出, 容易验证. 最后, 通过两个数值算例验证了该结果的有效性及可行性. 该判据对丰富与完善中立型神经网络的稳定性理论体系, 具有积极的意义.     

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.     

New stability criteria for neutral-type Cohen–Grossberg neural networks with discrete and distributed delays

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results.