New predefined-time stability results of impulsive systems with time-varying impulse strength and its application to synchronization of delayed BAM neural networks

In this paper, the predefined-time synchronization of BAM neural networks with hybrid impulsive effects and time-varying delays is explored. First, based on the improved Lyapunov function method, two novel predefined-time stability lemmas of impulsive dynamical systems are given, in which the derivative of Lyapunov function can be negative definite or indefinite. Second, different from previous studies on constant impulse strength, we consider the impulse strength as a time-varying function, which can take different values at different moments and allow for the coexistence of both stabilizing and destabilizing impulses simultaneously. Then, two novel controllers are designed, and some sufficient conditions are derived to ensure predefined-time synchronization of the established system. Finally, the effectiveness of the obtained criteria is verified by a numerical simulation. The results show that the synchronized time can be adjusted according to actual needs and does not depend on the initial values and parameters of the system.