Stability Of Dynamical Neural Networks Research Articles

Robust stability of dynamical neural networks with multiple time delays: a review and new results

Robust stability of dynamical neural networks with multiple time delays: a review and new results

Novel criteria for global robust stability of dynamical neural networks with multiple time delays

This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example.

A new delay-independent condition for global robust stability of neural networks with time delays

This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results.

Dynamical Nonlinear Neural Networks with Perturbations Modeling and Global Robust Stability Analysis

paper is devoted to studying both the global and local stability of dynamical neural networks. In particular, it has focused on nonlinear neural networks with perturbation. Properties relating to asymptotic and exponential stability and instability have been detailed. This paper also looks at the robustness of neural networks to perturbations and examines if the related properties have been preserved. Circumstances for global and local exponential stability of nonlinear neural network dynamics have been studied. We mentioned that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks have been obtained. The Lyapunov's procedure has been used to analyze the stability property of nonlinear dynamical systems and many outcomes have been combined and generalized. A kind of Lyapunov's stability of the stable points of Hopfield neural network (HNN) have been proven, which means that if the initial state of the network is close enough to a stable point, then the network state will remain in a small neighborhood of the stable point. These stability results indicate the convergence of the memory process of HNN. The theoretical results are illustrated through a few problem cases for a nonlinear dynamical system with perturbation behavior. Keywordserturbed nonlinear systems, Hopfield neural network,

ℒ2—ℒ∞ learning of dynamic neural networks

This paper proposes an ℒ2—ℒ∞ learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the ℒ2—ℒ∞ learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an ℒ2—ℒ∞ induced norm constraint. It is shown that the design of the ℒ2—ℒ∞ learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.

New results for robust stability of dynamical neural networks with discrete time delays

This paper deals with the global robust asymptotic stability of the equilibrium point of class of delayed neural networks having uncertain parameters whose values are unknown but bounded. By introducing a new upper bound norm for the interconnection matrix of the neural system and employing suitable Lyapunov functionals, we obtain new delay independent sufficient conditions for the uniqueness and global robust asymptotic stability of the equilibrium point. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. Some examples are constructed to compare the reported results with the related existing literature results.

A note on the global stability of dynamical neural networks

It is shown that the additive diagonal stability condition on the interconnection matrix of a neural network, together with the assumption that the activation functions are nondecreasing, guarantees the uniqueness of the equilibrium point. This condition, under the same assumption on the activation functions, is also shown to imply the local attractivity and local asymptotic stability of the equilibrium point, thus ensuring the global asymptotic stability (GAS) of the equilibrium point. The result obtained generalizes the previous results derived in the literature.

Input-to-state stability (ISS) analysis for dynamic neural networks

In this paper a novel approach to assess the stability of dynamic neural networks is presented. Using a Lyapunov function, we determine conditions to guarantee input-to-state stability (ISS) which also ensures global asymptotic stability (GAS). The applicability of these conditions is illustrated by two examples.

Stability analysis of dynamical neural networks

In this paper, we use the matrix measure technique to study the stability of dynamical neural networks. Testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given. It shows how a few well-known results can be unified and generalized in a straightforward way. Local exponential stability of a class of dynamical neural networks is also studied; we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks are obtained.

Global Stability of Dynamic Neural Networks

In this paper, some globally asymptotical stability criteria for the equilibrium states of a general class of discretetime dynamic neural networks with continuous states are presented using Lyapunov function approach. The neural networks are assumed to have the asymmetrical weight matrices throughout the paper. The globally diagonal Lyapunov function approach is used to study the global stability for a general class of discrete-time dynamic neural networks. Some novel stability conditions represented by either the existence of the positive diagonal solutions of the Lyapunov equations or some inequalities are given. Two examples are presented for demonstrating the effectiveness of the global stability conditions presented.