Global stability analysis in delayed cellular neural networks

In this paper, without assuming the boundedness, monotonicity, and differentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural network models with fixed time delays. The results are applicable to both symmetric and nonsymmetric interconnection matrices, and all continuous nonmonotonic neuron activation functions.     

Impulses-induced exponential stability in recurrent delayed neural networks

The present paper formulates and studies a model of recurrent neural networks with time-varying delays in the presence of impulsive connectivity among the neurons. This model can well describe practical architectures of more realistic neural networks. Some novel yet generic criteria for global exponential stability of such neural networks are derived by establishing an extended Halanay differential inequality on impulsive delayed dynamical systems. The distinctive feature of this work is to address exponential stability issues without a priori stability assumption for the corresponding delayed neural networks without impulses. It is shown that the impulses in neuronal connectivity play an important role in inducing global exponential stability of recurrent delayed neural networks even if it may be unstable or chaotic itself. Furthermore, example and simulation are given to illustrate the practical nature of the novel results.     

On the global stability of delayed neural networks

Lyapunov functional methods, combining with some inequality techniques, are employed to study the global asymptotic stability of delayed neural networks. Without assuming Lipschitz conditions on the activation functions, a new sufficient condition is established. Such criteria allows us to include non-Lipschitzian activation functions in the design of delayed neural networks. The result presented here is also discussed from the point of view of its relationship to some previous results.     

Exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks

This paper focuses on the problem of exponential stability in the sense of Lagrange for impulses in discrete-time delayed recurrent neural networks. By establishing a delayed impulsive discrete inequality and a novel difference inequality, combining with inequality techniques, some novel sufficient conditions are obtained to ensure exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks. Meanwhile, exponentially convergent scope of neural network is given. Finally, several numerical simulations are given to demonstrate the effectiveness of our results.     

On asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks

In this paper, we obtain some sufficient conditions for determining the asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks by utilizing the Lyapunov functional method. An example is given to show the validity of the results.     

On stability of delayed cellular neural networks with sigmoid output functions

In this paper a sufficient condition is presented to ensure the complete stability of delayed CNNs. Such a condition establishes a relation between the time delay and the parameters of the networks. Specially, for a given output function f(x) = tanh(x), we address a sufficient condition to ensure absolute convergence of system state.     

Global exponential periodicity and stability of memristor-based complex-valued delayed neural networks

This paper concentrates on the dynamical behaviours of memristor-based complex-valued delayed neural networks. By constructing the appropriate Lyapunov functional and utilising some inequality techniques, sufficient conditions are proposed to guarantee the existence and global exponential stability of the periodic solution of the considered system. The proposed results not only generalise some previously related literatures, but also are easy to be checked with the parameters of system itself. In addition, the theoretical results of this paper may be helpful in qualitative analysis for complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of the proposed results.     

An improved result for complete stability of delayed cellular neural networks

This paper provides a new sufficient condition for the complete stability of the delayed cellular neural networks. This condition imposes constraints on the parameters of the networks and the size of time delay. The linear matrix inequality approach plays an important role in the proof. Our result recovers the known results in the earlier literature as special cases. Finally, we give an example to illustrate the applicability of our main result.     

An analysis of global asymptotic stability of delayed cellular neural networks

In this paper, a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks (DCNNs). This condition imposes constraints on the feedback and delayed feedback matrices of a DCNN independently of the delay parameter. This result is also compared with the previous results derived in the literature.     

Global exponential stability results for delayed neural networks of neutral type

In this paper, by utilizing the Lyapunov–Krasovkii functional and combining with the linear-matrix inequality (LMI) approach, we analyse the global exponential stability of delayed neural networks of neutral type. In addition, the examples are provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

An improved global asymptotic stability criterion for delayed cellular neural networks

A new Lyapunov-Krasovskii functional is constructed for delayed cellular neural networks, and the S-procedure is employed to handle the nonlinearities. An improved global asymptotic stability criterion is also derived that is a generalization of, and an improvement over, previous results. Numerical examples demonstrate the effectiveness of the criterion.     

Global asymptotic stability of delayed neural networks with discontinuous neuron activations

This paper investigates a class of delayed neural networks whose neuron activations are modeled by discontinuous functions. By utilizing the Leray–Schauder fixed point theorem of multivalued version, the properties of M-matrix and generalized Lyapunov approach, we present some sufficient conditions to ensure the existence and global asymptotic stability of the state equilibrium point. Furthermore, the global convergence of the output solutions are also discussed. The assumptive conditions imposed on activation functions are allowed to be unbounded and nonmonotonic, which are less restrictive than previews works on the discontinuous or continuous neural networks. Hence, we improve and extend some existing results of other researchers. Finally, one numerical example is given to illustrate the effectiveness of the criteria proposed in this paper.     

New results concerning the exponential stability of delayed neural networks with impulses

Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here.     

Global robust stability of uncertain delayed neural networks with discontinuous neuron activation

This paper integrates global robust stability of uncertain delay neural networks with discontinuous activation. The activation function is unbounded and the uncertainties are norm bound. By the homotopy invariance and solution properties of the topological degree, the conditions for the existence of equilibrium are given out. Moreover, based on the Lyapunov–Krasovskii stability theory, the conditions of global robust stability for discontinuous delayed neural networks with uncertainties are presented in terms of linear matrix inequality. At last, an illustrative numerical example is provided to show the effectiveness of results given.     

Global exponential stability analysis of delayed Cohen--Grossberg neural networks with distributed delays

In this article, the global exponential stability problem of Cohen--Grossberg neural networks with both discrete-time delays and distributed delays is investigated. The existence and global stability for the unique equilibrium of the Cohen--Grossberg neural networks with distributed delays are achieved by using some new Lyapunov functionals, M-matrix theory and some analytic techniques, and some less restrictive conditions are obtained. An example is also worked out to validate the advantages of our results.     

Improved global robust asymptotic stability criteria for delayed cellular neural networks.

This paper considers the problem of global robust stability analysis of delayed cellular neural networks (DCNNs) with norm-bounded parameter uncertainties. In terms of a linear matrix inequality, a new sufficient condition ensuring a nominal DCNN to have a unique equilibrium point which is globally asymptotically stable is proposed. This condition is shown to be a generalization and improvement over some previous criteria. Based on the stability result, a robust stability condition is developed, which contains an existing robust stability result as a special case. An example is provided to demonstrate the reduced conservativeness of the proposed results.     

Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters

This paper deals with the global exponential stability in the mean square of fuzzy cellular neural networks with time-varying delays and Markovian jumping parameters. By constructing suitable Lyapunov functionals, we obtain several sufficient conditions which can be expressed in terms of linear matrix inequalities (LMIs). The proposed LMI results are computationally efficient as it can be solved numerically by using Matlab LMI toolbox. An example is given to show the effectiveness of the results.     

State estimation for delayed neural networks

In this letter, the state estimation problem is studied for neural networks with time-varying delays. The interconnection matrix and the activation functions are assumed to be norm-bounded. The problem addressed is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally exponentially stable. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. In particular, we derive the conditions for the existence of the desired estimators for the delayed neural networks. We also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities (LMIs). Finally, it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks. Numerical examples are included to illustrate the applicability of the proposed design method.     

Robustness of globally exponential stability of delayed neural networks in the presence of random disturbances

This paper analyzes the robustness of globally exponential stability of time-varying delayed neural networks (NNs) subjected to random disturbances. Given a globally exponentially stable neural network, and in the presence of noise, we quantify how much noise intensity that the delayed neural network can remain to be globally exponentially stable. We characterize the upper bounds of the noise intensity for the delayed NNs to sustain globally exponential stability. The upper bounds of parameter uncertainty intensity are characterized by using transcendental equation. A numerical example is provided to illustrate the theoretical result.     

Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis

In this paper, we obtain new sufficient conditions ensuring existence, uniqueness, and global asymptotic stability (GAS) of the equilibrium point for a general class of delayed neural networks (DNNs) via nonsmooth analysis, which makes full use of the Lipschitz property of functions defining DNNs. Based on this new tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then those results are applied to show that existence assumptions on the equilibrium point in some existing sufficient conditions ensuring GAS are actually unnecessary; and some strong assumptions such as the boundedness of activation functions in some other existing sufficient conditions can be actually dropped. Finally, we derive some new sufficient conditions which are easy to check. Comparison with some related existing results is conducted and advantages are illustrated with examples. Throughout our paper, spectral properties of the matrix (A + A/sup /spl tau//) play an important role, which is a distinguished feature from previous studies. Here, A and A/sup /spl tau// are, respectively, the feedback and the delayed feedback matrix defining the neural network under consideration.