Stochastic Stability of Markovian Neural Networks With Generally Hybrid Transition Rates.

Abstract

This article studies the problem of the stability for Markovian neural networks (MNNs) with time delay. The transition rate is considered to be generally hybrid, which treats those existing ones as its special cases. The introduced generally hybrid transition rates (GHTRs) make these systems more general and practical. Apropos of the GHTRs, a double-boundary approach rather than the traditional estimation method is introduced to make full use of the error information in GHTRs. In order to fully capture system information, a parameter-type-delay-dependent-matrix (PTDDM) approach is proposed, in which the PTDDM approach removes some zero components on slack matrices in previous works. Thus, the PTDDM approach can fully link the relationship among time delay and state-related vectors. Based on these ingredients, a novel stochastic stability condition is proposed for MNNs with GHTRs. A numerical example is illustrated to demonstrate the effectiveness of the proposed approaches.