Global exponential convergence and global convergence in finite time of non-autonomous discontinuous neural networks

The paper investigates global convergence of the solutions of a non-autonomous differential system with discontinuous right-hand side, arising from the description of the states of neurons in a general class of neural networks possessing discontinuous neuron activations in a time-varying situation. By exploring intrinsic features between the non-autonomous system and its asymptotic system, several novel sufficient conditions are derived which ensure global exponential convergence of the networks. Moreover, under some conditions, we prove that this networks possesses the property of global convergence in finite time, which cannot occur in smooth system. Our results can be easily verified and complement previous known criteria.