Pinning synchronization of delayed neural networks via Markov switched control

Abstract

This paper studies the pinning synchronization problems of delayed neural networks (DNNs) by Markov switched control, where appropriate neurons are chosen as the pinned control nodes and feedback control input is added at Markov jump time. Based on uniformly stable function (USF) and the infinitesimal generator of Markov process, some lemmas about $p$th moment exponential convergence for Markov switched systems are established, which are utilized to ensure that DNNs synchronize to a leader system in the mean square. Although some error subsystems may be divergent under pinning feedback input, then provided that the pinning feedback controller obeys Markov switching, the overall error system can achieve mean square convergence. Finally, numerical examples are given to illustrate the practicality of results.