Asynchronous Boundary Control of Markov Jump Neural Networks With Diffusion Terms

This article concerns with the asynchronous boundary control for a class of Markov jump reaction-diffusion neural networks (MJRDNNs). In consideration of nonsynchronous behavior between the system modes and controller modes, a novel asynchronous boundary control design is proposed for MJRDNNs. Based on the designed asynchronous boundary controller, a sufficient criterion is established to ensure the stochastic finite-time boundedness for the considered MJRDNNs by constructing a Lyapunov–Krasovskii functional and utilizing Wirtinger-type inequality. Then, a sufficient condition is acquired to guarantee that MJRDNNs are stochastic finite-time bounded with
$H_{\infty }$
performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design method.