Stability Of Retarded Neural Networks Of Neutral Type

Delayed neural networks of neutral-type are a kind of nonlinear systems whose differential expressions consist of not only the derivative terms of the current states but also those of the past states, which can further describe and model the dynamics for complex neural reactions. Recently, increaing attention has been paid to the problems of the retarded systems, fewer results of the stability for the neutral-type delayed neural networks are found in existing literature. In term of the applications in optimizing and controlling, it is desirable and preferable that the neural system has a unique equilibrium point, and it would be better for the neural network converges as fast as possible. In this dissertation, we study the asymptotic stability and exponential stability for the neutral-type delayed systems. The main contributions of this dissertation are as follows:①Global stability criteria for neural networks of retarded neutral-type are obtained.Several new delay-dependent asymptotical and exponential stability criteria with less conservation are established by employing Lyapunov-Krasovskii stability theorem, free weighting matrices method and LMI technique in virtue of the linearization of the corresponding model. The stability regions with respect to the delay parameters are formulated by applying the results proposed above.②The semi-free weighting matrices approach is made use of.Inspired by the free weighting matrices method, we consider the semi-free weighting matrices instead of the known free weighting matrices to express the relationship among the terms in the Leibniz-Newton formula to simplify the system synthesis and obtain less computation demand. Especially the semi-free weighting matrices approach is used to obtain the global exponential stability criteria for neural networks of neutral-type with constant delays. Some numerical examples are given to illustrate the effectiveness of our results.③Global exponential stability for neural networks of neutral-type with interval time-varying delays is analyzed.The interval time-varying delay is a time delay that varies in an interval whose the lower bound is not restricted to zero. To the best of our knowledge, there have been few results about interval time–varying delay for neural networks of neutral-type. By using the Lyapunov-Krasovskii stability theorem, the semi-free weighting matrices method and LMI technique, global exponential stability for interval time–varying delay for neural networks of neutral-type is investigated.