Observer-Based Asynchronous Boundary Stabilization for Stochastic Markovian Reaction-Diffusion Neural Networks

This work investigates the observer-based asynchronous boundary stabilization for a kind of stochastic Markovian reaction-diffusion neural networks with exogenous disturbances. Specifically, parameter uncertainties are considered in the drift item. First, a hidden Markov model is introduced that guarantees the observer modes run asynchronously with the system modes. It should be noted that the asynchronous observer constructed in this work only uses the boundary measurement information. Then a nonfragile asynchronous observer-based boundary controller is designed. Taking advantage of inequality techniques and stochastic analysis method, sufficient criterion is provided to satisfy input-to-state exponentially mean-square stability, and the asynchronous boundary observer/controller gains are further derived. As a special case, the synchronous observer-based boundary stabilization is also obtained. Finally, a numerical example is exploited to manifest the validity of the established results.