Xiaoxin Liao

Stability Analysis of Uncertain Neural Networks with Delay

The globally uniformly asymptotic stability of uncertain neural networks with time delay has been discussed in this paper.Using the Razumikhin-type theory and matrix analysis method, A sufficient criterion about globally asymptotic stability of the neural networks is obtained.

Global exponential stability in lagrange sense of continuous-time recurrent neural networks

In this paper, global exponential stability in Lagrange sense is further studied for continuous recurrent neural network with three different activation functions. According to the parameters of the system itself, detailed estimation of global exponential attractive set, and positive invariant set is presented without any hypothesis on existence. It is also verified that outside the global exponential attracting set; i.e., within the global attraction domain, there is no equilibrium point, periodic solution, almost periodic solution, and chaos attractor of the neural network. These theoretical analysis narrowed the search field of optimization computation and associative memories, provided convenience for application.

Exponential stability of delayed stochastic cellular neural networks

In view of the character of saturation linearity of output functions of neurons of the cellular neural networks, the method decomposing the state space to sub-regions is adopted to study almost sure exponential stability on delayed cellular neural networks which are in the noised environment. When perturbed terms in the model of the neural network satisfy Lipschitz condition, some algebraic criteria are obtained. The results obtained in this paper show that if an equilibrium of the neural network is the interior point of a sub-region, and an appropriate matrix related to this equilibrium has some stable degree to stabilize the perturbation, then the equilibrium of the delayed cellular neural network can still remain the property of exponential stability. All results in the paper is only to compute eigenvalues of matrices.

Almost sure exponential stability on interval stochastic neural networks with time-varying delays

Because of VLSI realization of artificial neural networks and measuring the elements of the circuits, noises coming from the circuits and the errors of the parameters of the network systems are therefore unavoidable. Making use of the stochastic version of Razumikhin theorem of stochastic functional differential equation, Lyapunov direct methods and matrix analysis,almost sure exponential stability on interval neural networks perturbed by white noises with time varying delays is examined, and some sufficient algebraic criteria which only depend on the systems’ parameters are given. For well designed deterministic neural networks, the results obtained in the paper also imply that how much tolerance against perturbation they have.

An LMI-Based approach to the global stability of bidirectional associative memory neural networks with variable delay

Based on the linear matrix inequality (LMI), new sufficient conditions on the global exponential stability and asymptotic stability of bidirectional associative memory neural networks with variable delay are presented, and exponential converging velocity index is estimated. Furthermore, the results in this paper are less conservative than the ones reported so far in the literature. One example is given to illustrate the feasibility of our main results.

Delay-dependent and delay-independent stability conditions of delayed cellular neural networks

By using the saturation linearity of the output functions of neurons in cellular neural networks, and by adopting the method of decomposing the state space to sub-regions, the mathematical equations of delayed cellular neural networks are rewritten to be the form of linear differential difference equations in the neighbourhood of each equilibrium, which is an interior point of some sub-region. Based on this linear form and by using the stability theory of linear differential difference equations and the tool of M-matrix, delay-dependent and delay-independent stability algebraic criteria are obtained. All results obtained in this paper need only to compute the eigenvalues of some matrices or to examine the matrices to be M-matrix or to verify some inequalities to be holden.

Exponential synchronization for a class of chaotic neural network with time-delay

The chaos synchronization between two time-delayed chaotic neural network has been discussed. Based the Lyapuov approaches, we have obtained some new synchronization conditions,the new results improve the earlier works.Numerical simulation is given to demonstrate the validness of the proposed results.

A generalized LMI-Based approach to the global exponential stability of recurrent neural networks with delay

A new theoretical result on the global exponential stability of recurrent neural networks with delay is presented. It should be noted that the activation functions of recurrent neural network do not require to be bounded. The presented criterion, which has the attractive feature of possessing the structure of linear matrix inequality (LMI), is a generalization and improvement over some previous criteria. A example is given to illustrate our results.