Global polynomial synchronization for quaternion-valued T–S fuzzy inertial neural networks via event-triggered control: A polynomial gain method

This work explores the global polynomial synchronization for a class of quaternion-valued Takagi–Sugeno fuzzy inertial neural networks based on event-triggered control. Firstly, the paper designs the fuzzy event-triggered controller with a polynomial gain, a unique approach to optimize the event-triggered mechanism. The non-reduced order and non-decomposition methods are applied to maintain computational efficiency without introducing new variables. Then, under static and dynamic event-triggered conditions, the system’s global polynomial synchronization is guaranteed by formulating a suitable delay-free Lyapunov functional and using quaternion properties and inequality techniques. Moreover, rigorous derivation is employed to verify a positive lower bound of any event-triggered interval, concluding that the system does not produce Zeno behavior. Finally, a numerical example and the application of image encryption and decryption are presented to strongly validate the reliability of the model and control mechanism in achieving global polynomial synchronization.