The Non-Fragile State Estimation For Time-delay Neural Networks Systems

In recent years,neural networks(NNs)system has been widely applied to the image processing,pattern recognition,associative memory process,the optimization problem and so on.This paper studies the stability analysis and state estimation problem of neural networks with time-delay.But it inevitably appears the phenomenon such as time-delay,nonlinearity and uncertainty in the actual system.In such a neural network model which has a large number of neurons and highly interconnected between neurons,it is often very difficult to get fully of all neurons state information,this requires people to approximate estimate the state of these neurons.Based on these considerations,it has very important theory value and practical significance to research the state estimation of a class of delay-time recursive neural network theory.In this paper,the stability and non-fragile state estimation problem of the neural network system is investigated,and a more relaxed stability condition is presented with less conservative results.The main results include four aspects as follow:Firstly,a non-fragile state estimator for discrete neural network systems with constant time-delay is designed.Based on the Lyapunov-Krsasovskii stability theory and some transformation skills of matrix inequalities,sufficient conditions of asymptotic stability are given for neural network system with time-delay in the form of linear matrix inequality(LMI),and the state estimator gain are obtained.Secondly,the state estimation problem is studied that there exist uncertainty factors in the system model and neural network estimator model at the same time.By employing the Lyapunov stability theory and the matrix analysis technique,a sufficient condition is established to ensure that the dynamics of the estimation error achieves the asymptotic stability for all admissible parameter uncertainties as well as gain variations.Under this condition,the implementation of a non-fragile state estimator is transformed into solving a feasible solution of the corresponding LMIs.Thirdly,considering the network redundancy phenomenon of time-driven mechanism,the event-driven mechanism is introduced to the discrete time-delay neural network,and it is effective to solve the problem.By constructing new Lyapunov function,the delay-dependent sufficient conditions are obtained to guarantee the system to be globally asymptotically stable in the mean square,and explicit expression of the desired estimators is given in terms of the solution to a linear matrix inequality.Finally,a non-fragile state estimation problem is studied for neural network system with the probability distribution of time-delay.Bernoulli stochastic processes and the Brownian motion that are independent of each other are utilized to respectively depict the probability distribution of time-varying delay and randomly occurring nonlinear disturbances.By designing a non-fragile state estimator,the delay-dependent sufficient condition are established that guarantee the stability of the system,and corresponding estimator gain matrix is obtained by solving an LMI.