Noise-Induced Stabilization of the Recurrent Neural Networks With Mixed Time-Varying Delays and Markovian-Switching Parameters

Abstract

The stabilization of recurrent neural networks with mixed time-varying delays and Markovian-switching parameters by noise is discussed. First, a new result is given for the existence of unique states of recurrent neural networks (NNs) with mixed time-varying delays and Markovian-switching parameters in the presence of noise, without the need to satisfy the linear growth conditions required by general stochastic Markovian-switching systems. Next, a delay-dependent condition for stabilization of concerned recurrent NNs is derived by applying the ltd formula, the Gronwall inequality, the law of large numbers, and the ergodic property of Markovian chain. The results show that there always exists an appropriate white noise such that any recurrent NNs with mixed time-varying delays and Markovian-switching parameters can be exponentially stabilized by noise if the delays are sufficiently small.