Global Polynomial Synchronization of Quaternion‐Valued Inertial Neural Networks With Proportional Delay and Mismatched Parameters

ABSTRACT This paper investigates the global polynomial synchronization of the quaternion‐valued inertial neural networks with proportional delay and mismatched parameters. The global polynomial synchronization of neural networks is guaranteed by constructing the suitable Lyapunov functional and controller, utilizing nonreduction and nondecomposition methods. Notably, the Lyapunov functional established is delay‐free, and choosing the appropriate norm of the quaternion vectors can more effectively reduce the Lyapunov functional. Moreover, some quaternion properties are applied to explore the global polynomial synchronization problem of quaternion‐valued inertial neural networks, which avoids quaternion decomposition. Finally, we validate the conclusions with the numerical simulation.