Asynchronous Boundary Stabilization of Stochastic Markovian Reaction–Diffusion Neural Networks With Mode-Dependent Delays

This article tackles asynchronous control issue for a class of stochastic Markovian reaction-diffusion neural networks with mode-dependent delays (MDDs). Taking into account the spatio-temporal distribution of such networks, we propose a boundary control (BC) scheme combined with asynchronous control to reduce control implementation cost and overcome environmental constraint. By incorporating a hidden Markov model to manage the mode asynchrony, we develop an integral asynchronous boundary controller for Neumann boundary conditions, as well as an innovative one for Dirichlet boundary conditions. We then derive an exponential stability criterion specific to MDDs and introduce a novel asynchronous BC synthesis approach. Additionally, we extend our findings to the leader-follower synchronization of these neural networks. The validity, superiority, and practicality of the proposed control design approach are demonstrated via three numerical examples, respectively.