New fixed-time stability criterion and fixed-time synchronization of neural networks via non-chattering control

Based on the framework of Filippov solution, a non-chattering controller is presented to realize the fixed-time (FXT) stability for a nonlinear system with the discontinuous activation function. First, a novel FXT stability criterion is established through the reduction to absurdity, and the settling time is estimated. Then, by building two controllers without chattering, sufficient conditions are obtained to ensure the FXT synchronization of the drive-response system. Moreover, compared with the existing results, the FXT obtained here is less conservative and more accurate. Finally, the validity of the proposed methods is provided by two numerical examples.