Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays

In this Letter, the mean-square exponential stability problem for stochastic Hopfield neural networks with both discrete and distributed time-varying delays is investigated. By choosing a modified Lyapunov-Krasovskii functional, a delay-dependent criterion is established such that the stochastic neural network is mean-square exponentially stable. The derivative of discrete time-varying delay h(t) satisfies and the decay rate β can be any finite positive value without any other constraints. The assumptions given in this Letter are more general than the conventional assumptions (i.e., and β satisfies a transcendental equation or an inequality). Finally, numerical examples are provided to illustrate the effectiveness of the proposed sufficient conditions.     

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ‘delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.     

Stability analysis of delayed genetic regulatory networks with stochastic disturbances

This Letter considers the problem of stability analysis of a class of delayed genetic regulatory networks with stochastic disturbances. The delays are assumed to be time-varying and bounded. By utilizing Itô's differential formula and Lyapunov-Krasovskii functionals, delay-range-dependent and rate-dependent (rate-independent) stability criteria are proposed in terms of linear matrices inequalities. An important feature of the proposed results is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another important feature is that the obtained stability conditions are less conservative than certain existing ones in the literature due to introducing some appropriate free-weighting matrices. A simulation example is employed to illustrate the applicability and effectiveness of the proposed methods.     

Improved delay-dependent stability criterion for neural networks with time-varying delays

In this Letter, the problem of stability analysis for neural networks with time-varying delays is considered. By constructing a new Lyapunov functional, a new delay-dependent stability criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criterion.     

Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays

This Letter deals with the problem of delay-dependent robust exponential stability in mean square for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-varying delays. Based on Lyapunov-Krasovskii functional and the stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Because of introducing some free-weighting matrices to develop the stability criteria, the proposed stability conditions have less conservatism. Numerical examples are given to illustrate the effectiveness of our results.     

Stability analysis of neural networks with interval time-varying delays

The global exponential stability is investigated for neural networks with interval time-varying delays. Based on the Leibniz-Newton formula and linear matrix inequality technique, delay-dependent stability criteria are proposed to guarantee the exponential stability of neural networks with interval time-varying delays. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing ones in the literature.     

An LMI approach to asymptotical stability of multi-delayed neural networks

In this paper, some criteria are derived for global asymptotic stability of a class of neural networks with multiple constant or time-varying delays. Based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach, some delay-independent criteria for neural networks with multiple constant delays and delay-dependent criteria for neural networks with multiple time-varying delays are provided to guarantee global asymptotic stability of these networks. The main results are generalizations of some recent results reported in the literature.     

Stochastic asymptotic stability of Markovian jumping neural networks with Markov mode estimation and mode-dependent delays

In a previous work [Z.D. Wang, Y.R. Liu, L. Yu, X.H. Liu, Phys. Lett. A 356 (2006) 346] an exponential stability analysis for a class of Markovian jumping neural networks (MJNNs) was presented. In this Letter we employ the same technique to extend the results for MJNNs with time-varying delays and mode estimation, appropriate for active fault-tolerant control systems.     

Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties

This Letter deals with the problem of exponential stability for a class of delayed Hopfield neural networks. Based on augmented parameter-dependent Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stability are obtained for two cases of time-varying delays: the delays are differentiable and have an upper bound of the delay-derivatives, and the delays are bounded but not necessary to be differentiable. The conditions are presented in terms of linear matrix inequalities, which allow to compute simultaneously two bounds that characterize the exponential stability rate of the solution. Numerical examples are included to illustrate the effectiveness of our results.     

Synchronization stability of general complex dynamical networks with time-varying delays

The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The novel delay-dependent criteria in terms of linear matrix inequalities (LMI) are derived based on free-weighting matrices technique and appropriate Lyapunov functional proposed recently. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria.     

Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Synchronization in a class of weighted complex networks with coupling delays

It is commonly accepted that realistic networks can display not only a complex topological structure, but also a heterogeneous distribution of connection weights. In addition, time delay is inevitable because the information spreading through a complex network is characterized by the finite speeds of signal transmission over a distance. Weighted complex networks with coupling delays have been gaining increasing attention in various fields of science and engineering. Some of the topics of most concern in the field of weighted complex networks are finding how the synchronizability depends on various parameters of the network including the coupling strength, weight distribution and delay. On the basis of the theory of asymptotic stability of linear time-delay systems with complex coefficients, the synchronization stability of weighted complex dynamical networks with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of the synchronization state. Finally, an example is given as an illustration testing the theoretical results.     

Robust stability of bidirectional associative memory neural networks with time delays

Based on the Lyapunov–Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.     

Global exponential stability of reaction diffusion neural networks with discrete and distributed time-varying delays

This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays.By constructing a more general type of Lyapunov-Krasovskii functional combined with a free-weighting matrix approach and analysis techniques,delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities.The obtained results are dependent on the size of the time-varying delays and the measure of the space,which are usually less conservative than delay-independent and space-independent ones.These results are easy to check,and improve upon the existing stability results.Some remarks are given to show the advantages of the obtained results over the previous results.A numerical example has been presented to show the usefulness of the derived linear matrix inequality(LMI)-based stability conditions.     

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.     

Global exponential stability for discrete-time neural networks with variable delays

This Letter provides new exponential stability criteria for discrete-time neural networks with variable delays. The main technique is to reduce exponential convergence estimation of the neural network solution to that of one component of the corresponding solution by constructing Lyapunov function based on M-matrix. By introducing the tuning parameter diagonal matrix, the delay-independent and delay-dependent exponential stability conditions have been unified in the same mathematical formula. The effectiveness of the new results are illustrated by three examples.     

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.     

Leader-following consensus control for networked multi-teleoperator systems with interval time-varying communication delays

We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov-Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities, which can easily be solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods.     

Novel criteria of synchronization stability in complex networks with coupling delays

Complex networks are wide spread in the real world, arising in fields as disparate as sociology, physics and biology. The information spreading through a complex network is often associated with time delays due to the finite speeds of signal transmission over a distance. Hence, complex networks with coupling delays have gained increasing attention in various fields of science and engineering today. In this paper, based on the theory of asymptotic stability of linear time-delay systems, synchronization stability in complex dynamical networks with coupling delays is investigated, and we derive novel criteria of synchronization state for both delay-independent and delay-dependent stabilities. As illustrative examples, we use the networks with coupling delays and a given coupling scheme to test the theoretical results.     

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional

In this paper,new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived.The stability conditions are represented in terms of linear matrix inequalities(LMIs) by constructing new Lyapunov-Krasovskii functional.The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints.The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound.Numerical examples are presented to show the effectiveness of the proposed method.