Neutral Stochastic Neural Networks Research Articles

Adaptive exponential synchronization of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions

<p>In this paper, we investigated the adaptive exponential synchronization problem of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions. A stochastic variable with a Bernoulli distribution was utilized to transform the information regarding probabilistic delays into a model featuring deterministic time delays and stochastic parameters. In the context of adaptive controllers, exponential synchronization conditions depending on the delay, noise intensity, and impulse factor were derived using Lyapunov-Krasovskii functions, the nature of Lévy noise, and some inequality methods. To provide further support for the proposed approach, two numerical illustrations were presented.</p>

Stabilization of highly nonlinear hybrid neutral stochastic neural networks with time-varying delays by variable-delay feedback control

Stabilization of highly nonlinear hybrid neutral stochastic neural networks with time-varying delays by variable-delay feedback control

Analysis of Exponential Stability for Neutral Stochastic Cohen-Grossberg Neural Networks with Mixed Delays

This paper is concerned with the mean-square exponential input-to-state stability problem for a class of stochastic Cohen-Grossberg neural networks. Different from prior works, neutral terms and mixed delays are discussed in our system. By employing the Lyapunov-Krasovskii functional method, Itô formula, Dynkin formula, and stochastic analysis theory, we obtain some novel sufficient conditions to ensure that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are given to illustrate the correctness of the theoretical results.

Stability and Dissipativity Analysis for Neutral Type Stochastic Markovian Jump Static Neural Networks with Time Delays

Abstract This paper studies the global asymptotic stability and dissipativity problem for a class of neutral type stochastic Markovian Jump Static Neural Networks (NTSMJSNNs) with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii Functional (LKF) with some augmented delay-dependent terms and by using integral inequalities to bound the derivative of the integral terms, some new sufficient conditions have been obtained, which ensure that the global asymptotic stability in the mean square. The results obtained in this paper are expressed in terms of Strict Linear Matrix Inequalities (LMIs), whose feasible solutions can be verified by effective MATLAB LMI control toolbox. Finally, examples and simulations are given to show the validity and advantages of the proposed results.

Exponential passivity conditions on neutral stochastic neural networks with leakage delay and partially unknown transition probabilities in Markovian jump

This paper studies the problem of exponential passivity for neutral stochastic neural networks (NSNN) with leakage delay and Markovian jump. The Markovian jump has partially unknown transition probabilities (PUTPs). By utilizing the Itô differential rule, choosing a suitable Lyapunov–Krasovskii functional and combining with the inequality technique, the sufficient delay-dependent exponential passivity criteria are obtained. These sufficient conditions are provided in the form of linear matrix inequalities (LMIs), which can be easily solved by LMI toolbox in Matlab. Finally, two simulated numerical examples are discussed in detail to illustrate the effectiveness of the established results.

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications.

In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.

Mean-square exponential input-to-state stability for neutral stochastic neural networks with mixed delays

This paper is concerned with the input-to-state stability problem of a class of neutral stochastic neural networks. The stochastic neural networks that we consider contain both neutral terms and mixed delays. By utilizing the Lyapunov–Krasovskii functional method, stochastic analysis techniques and It o^׳s formula, some sufficient conditions are derived to ensure the mean-square exponential input-to-state stability of the addressed system. Two numerical examples and their simulations are given to illustrate the effectiveness of the derived results.

Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks

The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov–Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.

Robust stability and $$H_{\infty}$$ H ∞ filter design for neutral stochastic neural networks with parameter uncertainties and time-varying delay

This paper is concerned with the problem of robust stability and \(H_{\infty}\) filter design for neutral stochastic neural networks with parameter uncertainties and time-varying delay. The parameter uncertainties are assumed to be norm-bounded. With the Lyapunov-krasovskii theory, several delay-dependent stability conditions are obtained in terms of liner matrix inequalities(LMIs). Based on the obtained stability criteria, some sufficient conditions for the existence of the robust \(H_{\infty}\) filter are derived. The obtained results ensure the robust stability and a prescribed \(H_{\infty}\) performance level of the filtering error systems for all admissible uncertainties. Finally, two numerical examples are given. One is provided to demonstrate the stability analysis results in this paper are less conservative than some existing results. The other is provided to illustrate the effectiveness of the filter design method.

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.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results.

Mean Square Asymptotic Stability of Neutral Stochastic Neutral Networks with Multiple Time-Varying Delays

The paper considers the problems of almost surely asymptotic stability for neutral stochastic neural networks with multiple time-varying delays. By applying Lyapunov functional method and differential inequality techniques, new sufficient conditions ensuring the existence and almost surely asymptotic stability of neutral stochastic neural networks with multiple time-varying delays are established. The results are shown to be generalizations of some previously published results and are less conservative than existing results.

Delay-interval-dependent robust-stability criteria for neutral stochastic neural networks with polytopic and linear fractional uncertainties

In this paper, the delay-interval-dependent robust stability is studied for a class of neutral stochastic neural networks with time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the upper bound is known and the lower bound is not restricted to zero. For the neural networks under study, the uncertainty includes polytopic uncertainty and linear fractional norm-bounded uncertainty. Sufficient conditions for the stability of the addressed neutral stochastic neural networks with time-varying delays are established by employing the proper Lyapunov–Krasovskii functional, a combination of the stochastic analysis theory, some inequality techniques and new linear matrix inequality (LMI). Finally, three numerical examples are provided to demonstrate less conservatism and effectiveness of the proposed LMI conditions.

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.

Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays

In this paper, the global asymptotic stability is investigated for a class of neutral stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stability theory and stochastic analysis approaches, delay-dependent criteria are derived to ensure the global, robust, asymptotic stability of the addressed system in the mean square for all admissible parameter uncertainties. The criteria can be checked easily by the LMI Control Toolbox in Matlab. A numerical example is given to illustrate the feasibility and effectiveness of the results.