Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks

Abstract

This paper investigates, through designing an event-triggered sampled-data mechanism, the stochastic stabilization of Markovian jump quaternion-valued neural networks (QVNNs) with partially unknown transition probabilities. First, since the multiplication of quaternions is not commutative, the Markovian jump QVNNs are decomposed into four real-valued neural networks. Then, by constructing a novel augmented Lyapunov–Krasovskii functional (LKF), it is containing more hybrid features, in which concerning the practical sampling pattern, and using the convex combinatorial optimization and inequality technique, the stabilization condition is proposed in the form of linear matrix inequalities (LMIs). Furthermore, the desired event-triggered sampled-data controller gains are obtained for the closed-loop Markovian jump QVNNs with partially unknown transition probability. Finally, the viability and validness of the obtained results are confirmed via three numerical examples.