Fixed-time pinning-controlled synchronization for coupled delayed neural networks with discontinuous activations.

This paper deals with the fixed-time synchronization problem of coupled delayed neural networks with discontinuous activations. Based on pinning control, a discontinuous controller is firstly proposed to guarantee that coupled neural networks achieve synchronization with a desired trajectory in finite time. Then, a discontinuous fixed-time controller is designed. With the fixed-time controller, the settling time can be estimated regardless of initial conditions. By providing a topology-dependent Lyapunov function, some criteria of finite-/fixed-time synchronization are derived. Finally, two numerical examples are given to show the effectiveness of the proposed controllers.