Global robust exponential stability of delayed neural networks: An LMI approach

In this paper, the problems of determining the robust exponential stability and estimating the exponential convergence rate for neural networks with parametric uncertainties and time delay are studied. Based on Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique, some delay-dependent criteria are derived to guarantee global robust exponential stability. The exponential convergence rate can be easily estimated via these criteria.     

A new global stability result for delayed neural networks

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new sufficient condition is presented for the global asymptotic stability of delayed neural networks. The condition contains and improves some of the previous results in the earlier references.     

Global robust stability of delayed recurrent neural networks

This paper is concerned with the global robust stability of a class of delayed interval recurrent neural networks which contain time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. A new sufficient condition is presented for the existence, uniqueness, and global robust stability of equilibria for interval neural networks with time delays by constructing Lyapunov functional and using matrix-norm inequality. An error is corrected in an earlier publication, and an example is given to show the effectiveness of the obtained results.     

A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach

In this paper, global asymptotic stability is discussed for neural networks with time-varying delay. Several new criteria in matrix inequality form are given to ascertain the uniqueness and global asymptotic stability of equilibrium point for neural networks with time-varying delay based on Lyapunov method and Linear Matrix Inequality (LMI) technique. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using recently developed interior-point algorithm. In addition, the proposed results generalize and improve previous works. The obtained criteria also combine two existing conditions into one generalized condition in matrix form. An illustrative example is also given to demonstrate the effectiveness of the proposed results.     

Delay-dependent stability criterion for delayed Hopfield neural networks

In this paper, a new Lyapunov–Krasovskii functional is constructed for delayed Hopfield neural networks, and several free-weighting matrices and S-procedure are employed to derive the delay-dependent stability criterion. The derived criterion is formulated in terms of linear matrix inequality (LMI). A numerical example is given to demonstrate the effectiveness and less conservativeness of the presented criterion.     

A semi-free weighting matrices approach for neutral-type delayed neural networks

In this paper, a new approach is proposed for stability issues of neutral-type neural networks (DNNs) with constant delay. First, the semi-free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the Leibniz–Newton formula to simplify the system synthesis and to obtain less computation demand. Second, global exponential stability conditions which are less conservative and restrictive than the known results are derived. At the same time, based on the above approach, fewer variable matrices are introduced in the construction of the Lyapunov functional and augmented Lyapunov functional. Two examples are given to show their effectiveness and advantages over others.     

A new criterion for global robust stability of interval delayed neural networks

A novel criterion for the global robust stability of Hopfield-type interval neural networks with delay is presented. An example showing the effectiveness of the present criterion is given.     

Improved global robust stability criterion for delayed neural networks

A criterion for the uniqueness and global robust stability of the equilibrium point of interval Hopfield-type delayed neural networks is presented. The criterion is a marked improvement over a recent criterion due to Cao, Huang and Qu.     

Delay-dependent global stability condition for delayed Hopfield neural networks

In this paper, by utilizing the Lyapunov functional method and combining with the linear matrix inequality approach, we analyze the global asymptotic stability of delayed Hopfield neural networks (HNNs). A new sufficient condition ensuring the global stability of the unique equilibrium point of delayed HNNs is obtained, which is dependent on the size of delays. This condition is less restrictive and conservative than that given in the earlier references. In addition, an example is also provided to illustrate the applicability of the result.     

Delay-dependent global asymptotic stability for delayed cellular neural networks

In this note, we address the problem of the existence of a unique equilibrium point and present delay-dependent global asymptotical stability for cellular neural networks with time-delay. The LMI-based criteria are checkable easily. An example illustrates that the proposed conditions provide useful and less conservative results for the problem.     

Novel results for global robust stability of delayed neural networks

This paper investigates the global robust convergence properties of continuous-time neural networks with discrete time delays. By employing suitable Lyapunov functionals, some sufficient conditions for the existence, uniqueness and global robust asymptotic stability of the equilibrium point are derived. The conditions can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are also given to compare our results with previous robust stability results derived in the literature.     

Exponential stability of delayed fuzzy cellular neural networks with diffusion

The exponential stability of delayed fuzzy cellular neural networks (FCNN) with diffusion is investigated. Exponential stability, significant for applications of neural networks, is obtained under conditions that are easily verified by a new approach. Earlier results on the exponential stability of FCNN with time-dependent delay, a special case of the model studied in this paper, are improved without using the time-varying term condition: dτ(t)/dt < μ.     

Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach

In this paper, the problems of exponential convergence and the exponential stability of the periodic solution for a general class of non-autonomous competitive–cooperative neural networks are analyzed via the decomposition approach. The idea is to divide the connection weights into inhibitory or excitatory types and thereby to embed a competitive–cooperative delayed neural network into an augmented cooperative delay system through a symmetric transformation. Some simple necessary and sufficient conditions are derived to ensure the componentwise exponential convergence and the exponential stability of the periodic solution of the considered neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice.     

Improved asymptotic stability analysis for uncertain delayed state neural networks

This paper presents a new linear matrix inequality (LMI) based approach to the stability analysis of artificial neural networks (ANN) subject to time-delay and polytope-bounded uncertainties in the parameters. The main objective is to propose a less conservative condition to the stability analysis using the Gu’s discretized Lyapunov–Krasovskii functional theory and an alternative strategy to introduce slack matrices. Two computer simulations examples are performed to support the theoretical predictions. Particularly, in the first example, the Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability. The second example is presented to illustrate how the proposed approach can provide better stability performance when compared to other ones in the literature.     

An improved global exponential stability criterion for delayed neural networks

Based on Lyapunov–Krasovskii stability theory and the linear matrix inequality (LMI) technique, a criterion is derived to guarantee the global exponential stability of the class of delayed neural networks with time-varying delays, which generalizes and improves previous results. Numerical examples demonstrate the effectiveness of the criterion.     

New delay-dependent global asymptotic stability criteria of delayed Hopfield neural networks

In this paper, the global asymptotic stability of Hopfield neural networks (HNNs) with delays is investigated by utilizing Lyapunov functional method and the linear matrix inequality (LMI) technique. Distinct difference from other analytical approaches lies in “linearization” of the neural network model, by which the considered neural network model is transformed into a linear time-variant system. Then, a process, which is called parameterized first-order model transformation, is used to transform the linear system. Novel criteria for global asymptotic stability of the unique equilibrium point of delayed HNNs are obtained. The results are related to the size of delays. The obtained results are less conservative and restrictive than those established in the earlier references. Two numerical examples are given to show the effectiveness of our proposed method.     

Modified criteria for global robust stability of interval delayed neural networks

Two simple criteria for global robust stability of Hopfield-type interval neural networks with delay are presented. The criteria turn out to be modified versions of an earlier criterion due to Cao, Huang, and Qu. Examples show the effectiveness of the modified criteria. Numerical simulations are carried out to confirm the applicability of the modified criteria.     

Equilibrium and stability analysis of delayed neural networks under parameter uncertainties

This paper proposes new results for the existence, uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties. By using Lyapunov stability theorem and applying homeomorphism mapping theorem, new delay-independent stability criteria are obtained. The obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked. We also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature.     

Absolute exponential stability analysis of delayed bi-directional associative memory neural networks

The problem of absolute exponential stability for delayed bi-directional associative memory neural networks with time delay is investigated via Lyapunov stability theory. A new sufficient condition ensuring existence and uniqueness of equilibrium and its absolute exponential stability is derived. An illustrative example is given to demonstrate the effectiveness of the obtained results.     

New LMI-based criteria for global robust stability of delayed neural networks

Some novel, linear matrix inequality based, criteria for the uniqueness and global robust stability of the equilibrium point of Hopfield-type neural networks with delay are presented. A comparison of the present criteria with the previous criteria is made.