Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control

Abstract

This paper investigates the stochastic stabilization of Markov jump quaternion-valued neural networks (QVNNs) using a sampled-data control strategy. Firstly, Markov jump QVNNs are decomposed into two complex-valued systems using the plural decomposition method because the multiplication of quaternions is not commutative. Secondly, the existence and uniqueness of the equilibrium point of the Markov jump QVNNs is proved according to the theory of homeomorphism mapping. Thirdly, by choosing a suitable Lyapunov-Krasovskii functional and combining some inequality techniques, a new stochastic stability criterion is established for the Markov jump QVNNs. Based on this, several verifiable sufficient conditions for the stochastic stabilization of Markov jump QVNNs with sampled-data control are ensured. Finally, the correctness and effectiveness of the proposed method are verified by two numerical examples.