Mean-square exponential input-to-state stability of stochastic quaternion-valued neural networks with time-varying delays

In this paper, we first consider the stability problem for a class of stochastic quaternion-valued neural networks with time-varying delays. Next, we cannot explicitly decompose the quaternion-valued systems into equivalent real-valued systems; by using Lyapunov functional and stochastic analysis techniques, we can obtain sufficient conditions for mean-square exponential input-to-state stability of the quaternion-valued stochastic neural networks. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.