Research On Stability Analysis And Applications For Time-delayed Neural Networks

Owing to the inherent characteristics of the system and the existence of information transmission and other factors,time-delay phenomenon appears inevitably in many industrial processes.The existence of time delay usually results in many systems instable or even deterioration.In the system of neural networks,time delay is often found in the information transmission of neurons.the existence of time delay means that the rate of change of current state is not only dependent on the state of the current moment,but also related to the past moment or a period of the past.research on the stability of time-delay neural network has become a hot topic.On the other hand,in the practical engineering application,the each neuron state information is not always can obtain,normally only get the partial neuron measurement output,in order to get the information of the state of each neuron,the neural network state estimation problem is put forward,at the same time,designing a neural network state estimator and making the error system global stability.The contributions of this paper are summarized as follows:(1)For the problem of asymptotic stability for static neural networks with interval time-varying delay,based on the analysis of the problem of how to construct an augmented LK functional,the characteristics of the integral inequality are fully considered.A novel augmented Lyapunov-Krasovskii functional that contains vectors related to the integral inequality has been proposed.By using a further analytically improved Jensen inequality to deal with the integral term in the LK functional derivative,a less conservative delay-dependent stability criterion is derived in the form of linear matrix inequality(LMI).In order to verify the effective of the new augmented term to reduce the conservatism,we also give a comparison of the relevant stability criterion without using the new augmented term.At the same time,by ensuring the positive definiteness of the augmented LKF and using more information of the activation function,an improved stability criterion is further obtained.(2)Viaing consider both the construction of LKF and the estimation of signal integral term in the derivate of LKF,the problem of asymptotic stability for static neural networks with interval time-varying delays is analysed.To fully consider the new features of the improved Jensen inequality,a new augmented LK functional that contains some new state augmentation is proposed,and the triple integral term is also introduced to LKF.By using a new parameter dependent matrix inequality,a less conservative delay-dependent stability criterion is derived in terms of linear matrix inequality(LMI).Numerical examples are given to demonstrate the effectiveness of the proposed method.(3)Based on the analysis of the stability of static neural networks,we further survey the problem of H_?state estimation for static neural networks with time-varying,adopting the similar to the stability analysis of static recursive neural network processing method,an improved delay-dependent criterion is derived such that the estimation error system is globally asymptotically stable with a guaranteed H_?,and give the design method of state estimator,finally,a numerical example to verify the effectiveness of the proposed method.