Stability of Markovian Jump Bidirectional Associative Memory Neural Networks Under Lévy Noise and Discrete Observation

Abstract

The focus of this paper is to discuss the asymptotic stability and exponential stability problems of Markovian jump bidirectional associative memory neural networks with Lévy noise based on the discrete observation. Compared with the existing literature, this paper gives a weaker assumption regarding Lévy noise intensity functions. Furthermore, for the sake of solving difficulties caused by the discrete observation and Lévy noise, this paper designs a new Lyapunov-Krasovskii functional which not only depends on the discrete observation interval, but also intensity measures. In virtue of the M-matrix theory, three theorems are obtained ensuring the mean-square asymptotic stability and mean-square exponential stability of the trivial solution. Our theorems can not only deal with the discrete observation, but also with constant delays and variable time delays. Ultimately, two numerical examples are presented to illustrate the correctness of our theory findings.