Study On Global Stability Of Impulsive Delayed Neural Networks

As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dynamical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums and/or periodic solutions of delayed neural networks with impulses have been derived via Lyapunov-type function/functional approaches. A series of significative results have been obtained. This thesis mainly focuses on the global stability for three types of delayed neural networks with impulse. Specifically, the main contents are as follows:①Impulsive stabilization of delayed neural networksDue to the complexity and imperfection of impulsive control theory for delayed systems, to the best of the author's knowledge, stabilization of delayed systems via impulsive control approach has few results. In this thesis, the impulsive stabilization of the Hopfield-type delayed neural networks with and without uncertainty is investigated. A simple approach to the design of an impulsive controller is then presented. Two numerical examples are given for illustration of the theoretical results.②Delay-dependent and delay-independent stability criteria for cellular neural networks with impulses and delaySeveral novel delay-dependent and delay-independent asymptotical/exponential stability criteria with less restriction are established by employing parameterized first-order model transformation, Lyapunov-Krasovskii stability theorem and LMI technique in virtue of the linearization of considered model. The stability regions with respect to the delay parameters are formulated by applying the proposed results.③Effects of delay on exponential stability of cellular neural networks with delayWe investigate the global exponential stability conditions of the delayed neural networks with impulses by means of Lyapunov-like stability theorem, generalized Halanay inequalities. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse interval can be estimated by applying the proposed results. ④Existence and exponential stability of periodic solution of BAM Neural Networks with impulse and time-varying delayBy using the continuation theorem of coincidence degree theory and Lyapunov-Krasovskii function, the existence and global exponential stability of periodic solution for BAM model of neural network with impulses and time-delay are investigated. Sets of easily verifiable sufficient conditions are obtained for the existence and global stability of periodic solution. By contrast with the recent results in the literature, our results are much more universal application.⑤Existence and exponential stability of periodic solutions of impulsive cellular neural networks with delaysThe global periodicity of cellular neural network with impulses and time-delay is studied. Several conditions guaranteeing the existence, uniqueness, and global exponential stability of periodic solution are obtained, which improve and extend some previous results. The activation functions need not be differentiable, monotone or bounded. Some numerical examples are given to illustrate the effectiveness of our results⑥Exponential stability of periodic solution of cellular neural networks with impulses and leakage delayBecause time delays in the leakage terms are usually not easy to handle such delays have been rarely considered in the neural network community so far. By using a model transformation, a leakage delay dependent sufficient condition is derived. Systems contain many known systems as special cases and the sufficient conditions should also contain some existing results as special cases.