Pinning synchronization for markovian jump neural networks with uncertain impulsive effects

This work concentrates on synchronization of neural networks (NNs) with Markovian parameters, where the Markov chain has partially unknown transition probabilities (PUTP). Due to the existence of interfer-ence and noise in practice, we combine the uncertain variable with the complex coupling term as the impulsive disturbance of NNs. A corresponding mode-dependent pinning controller is designed to reduce the control costs, and synchronization error system is also derived, whose impulsive update state is listed separately. A sufficient condition of synchronization for NNs is completed by constructing a Lyapunov functional candidate and a series of iterations. Because the disturbance should avoid being too frequent to guarantee synchronization of NNs, the allowed minimum interval h of the impulsive disturbance is derived. Finally, the correctness and the superiority of the developed result are illustrated by a numerical example.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This work focuses on the synchronization problem of neural networks with Markovian parameters, where the partially unknown transition probabilities of the Markov chain are considered. Impulsive disturbances in the form of uncertain variables and complex coupling terms are introduced to account for interference and noise in practical systems. A mode-dependent pinning controller is designed to reduce control costs and a synchronization error system is derived. A sufficient condition for synchronization is established using a Lyapunov functional candidate and iterations. The allowed minimum interval of the impulsive disturbance is determined to avoid excessive disruption. Numerical examples are provided to illustrate the correctness and superiority of the proposed approach.