Global exponential estimates of delayed stochastic neural networks with Markovian switching.

Abstract

This paper is concerned with the global exponential estimating problem of delayed stochastic neural networks with Markovian switching. By fully taking the inherent characteristic of such kinds of neural networks into account, a novel stochastic Lyapunov functional is constructed in which as many as possible of the positive definite matrices are dependent on the system mode and a triple-integral term is introduced. Based on it, a delay- and mode-dependent criterion is derived under which not only the neural network is mean square exponentially stable but also the decay rate is well obtained. Moreover, it is shown that the established stability condition includes some existing ones as its special cases, and is thus less conservative. This approach is then extended to two more general cases where mode-dependent time-varying delays and parameter uncertainties are considered. Finally, three numerical examples are presented to demonstrate the performance and effectiveness of the developed approach.