Stability Of Delayed Neural Networks With Impulses

As an important part of the delayed large systems,the delayed neural network with impulses, which describes both the effect of delay on the current state and that of impulse on systems exhibits rich and colorful dynamical behaviors. In fact, it has become a powerful tool to characterize many phenomenons such as the immediate supply of pharmacy, frequency-signal processing system, and moving image processing. Recently, the dynamical issues of delayed neural networks with impulses have attracted worldwide attention, many interesting stability criteria for the equilibriums stability of delayed neural networks with impulses have been derived via Lyapunov-type function/functional approaches. In this dissertation, we study the asymptotic stability and exponential stability for delayed neural networks with impulses. The main contents of this dissertation are as follows:1. Stability criteria for delayed neural networks with impulsesSeveral new delay-dependent asymptotical and exponential stability criteria with less restriction are established by Lyapunov-Krasovskii stability theorem, employing parameterized first-order model transformation 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.2. The effects of impulse on stability of the cellular neural networksWe can obtain the asymptotical and exponential staility criteria of cellular neural networks, which can be expressed by the LMI. We fist linearize the model for the complexity of impulsive control theory for delayed systems, and then use the Lyapunov-like stability theorem and the general Halanay inequalities to get some asymptotical and exponential criteria. In the end, two numerical examples are given to illustrate the theoretical results that the unstable system can become stable because of the effect of impulses, and the stable system still hold stability under impulses.