Research On Stability And State Estimation For Neural Network Systems With Time Delay

Neural networks (NNs) have applied in a variety of areas, such as signal processing, pattern recognition, static image processing, associative memory, and combinatorial optimization in the past decades. In the real world, time delay is frequently encountered in NNs, it can easily reduce the transmission speed and even cause instability and oscillations in a system. So the study on the neural network systems with time delay is important in both theory and practice, and has thus been of great interest to a large number of researchers in the last few decades.The purpose of this dissertation is to study stability problem and present the more relaxed stability conditions for neural networks with time delays. In the first chapter, the development and the main method used to handle delayed neural networks are introduced. In the second chapter, a new augmented Lyapunov functional is proposed by considering the integral of the cross product term of the state, a delay-dependent criterion for delayed neural networks is obtained by employing free-weighting matrix approach. At the same time, the system is further studied by using the information of the delay fractioning methods. The new integral ineqoalities are used to obtain the more relaxed stability criterion for the delayed neural networks. In the third chapter, the delay-range-dependent stability problem for NNs is taken into account. The information of the lower and upper bounds of delay is used when constructing the Lyapunov functional, a new method that considers the relationship between the time-varying delay and its lower and upper bounds is proposed when estimating the upper bound of the derivative of Lyapunov functional. Less conservative delay-range-dependent stability criteria for NNs with time-varying interval delay are presented.The criteria are also extended to systems with time-varying structured uncertainties, the less conservative robust stability criterion is obtained. In the fourth chapter, by introducing a new Lyapunov function, the delay-dependent stability for continuous systems with two additive time-varying delay components is studied. a delay-dependent sufficient condition which can guarantee the system asymptotically stable is derived based on the term of linear matrix inequality (LMI) approach. An example shows that the conclusion obtained in this chapter has less conservativeness than the existing ones. In the fifth chapter, the delay-dependent state estimation problem for neural networks with time-varying delay is investigated. A delay-depenent criterion is established to estimate the neuron states through avaliable output measurements, such that the dynamics of the estiamtion error is globally exponentially stable.The criterion is formulated in LMI, and the gain matrix of state estimation is computed.