Study On Asymptotic And Robust Stability Of Delayed Neural Networks

The neural network, as a large-scale complex system, exhibits the rich and colorful dynamical behaviors. In the recent twenty years, duo to its important and potential applications in associative memory, pattern recognition, optimizing problems and so on, the dynamical issues of delayed neural networks have been investigated intensively. In order to analyze and apply easily, the transmission delays are ignored in modeling for most of system. But it is demonstrated by theories and practices that time delay is unavoidable. At the same time, time delays may affect the stability of the system, even lead to instability, oscillation or chaos phenomena. Recently, delayed neural networks have attracted a large number of researchers, and a series of significative results have been established.This dissertation focuses on the exponential and asymptotical and robust stability for several delayed system. The main achievements and originality contained in this dissertation are as follows:1. Asymptotical stability analysis for recurrent neural networks with time-varying delaysThe problem of the globally asymptotical stability of recurrent neural networks with time varying delay is investigated. By transforming the delayed neural model to describer model and then employing Lapunov Krasovskii stability theorem, linear matrix inequality (LMI) technique, S procedure and some algebraic inequality method, a new sufficient condition, which is determined by the coefficients of the model and includes more tuning parameters, for determining the global asymptotical stability of recurrent neural networks with time-varying delay is derived. The proposed result is further applied to two special cases: cellular neural network model with time delay and recurrent neural networks with constant delays. It is shown by theoretical analysis and computer simulations that the presented results provide several new sufficient conditions for the asymptotical stability of the investigated delayed neural network model.2. Delay-interval dependent stability of recurrent neural networks with time-varying delayThe delay-interval-dependent stability of the equilibrium point of a general class of recurrent neural networks with time-varying delays that may exclude zero has been studied. By constructing the appropriate Lyapunov-Krasovskii functional, two sufficient conditions ensuring the global asymptotic stability of the equilibrium point of such networks with interval time-varying delays are established.3. Delay-dependent robust stability analysis for interval linear time-variant systems with delays and application to delayed neural networksSome delay-dependent robust asymptotical stability criteria for uncertain linear time-variant systems with multiple delays are established by means of parameterized first-order model transformation and the transformation of the interval uncertainty into the norm-bounded uncertainty. The stable regions with respect to the delay parameters are also formulated. Based on these results, we investigate the stability issue of a class of delayed neural networks that can be transformed into linear time-variant systems, and then several new global asymptotical stability criteria are exploited. 4. Stabilizing effects of impulses in delayed BAM neural networksThe stabilizing effects of impulses in delayed bidirectional associative memory (DBAM) neural networks when its continuous component does not convergeasymptotically to the equilibrium point have been studied. A general criterion, which characterizes the aggregated effects of the impulse and the deviation of its continuous component from the equilibrium point on the exponential stability of the considered DBAM, is established by using Lyapunov-Razumikhin technique.5. Stability analysis of BAM neural networks with impulse and delaysWe further studies the global exponential stability of the equilibrium point of the delayed bidirectional associative memory (DBAM) neural networks with impulse effects. Several results characterizing the aggregated effects of impulse and dynamical property of the impulse-free DBAM on the exponential stability of the considered DBAM have been established. It is shown that the impulsive DBAM will preserve the global exponential stability of the impulse-free DBAM even if the impulses have enlarging effects on the states of neurons.6. On hybrid impulsive and switching neural networksWe also formulate and study a model of hybrid impulsive and switching Hopfield neural networks. Using switching Lyapunov functions and a generalized Halanay inequality, some general criteria, which characterize the impulse effect and switching effect in aggregated form, for asymptotic and exponential stability of such neural networks with arbitrary and conditioned impulsive switching are established.