Bam Neural Network Robust Stability Analysis

The bi-directional associate memory neural networks not only has the properties that are similar in some aspects to general neural networks,but also have its own unique characteristics. In this paper, we study the problem of the existence, uniqueness and stability of equilibrium point for bi-directional associate memory neural networks systems. The main purpose is to discuss the existence, uniqueness, asymptotic stability and robust stability conditions for bi-directional associate memory neural networks systems with continuous time-delay and distributed delay. Some results obtained are improved and perfected. This paper mainly includes the following four parts:First, we research on the problem of the existence of equilibrium point for bi-directional associate memory neural networks systems with continuous time-delay and distributed delay. By constructing a mapping and utilizing Brouwer fixed point theorem, we prove the existence of equilibrium point for bi-directional associate memory neural networks systems with continuous time delay and distributed delay.Second, we research on the problem of the uniqueness of equilibrium point for bi-directional associate memory neural networks systems with continuous time delay and distributed delay. Using the technique of analyzing inequality, the sufficient condition was derived for the uniqueness equilibrium point.Then we research on the problem of asymptotic stability and robust stability of equilibrium point for bi-directional associate memory neural networksystems with continuous time-delay and distributed delay. We use Lyapunov functional method, linear matrix inequalities method and Schur theory. The asymptotic stability and robust stability sufficient conditions are derived.Finally, it implies the effectiveness of the proposed results through two examples.