The problem of global robust asymptotical stability for a class of Takagi-Sugeno fuzzy neural networks (TSFNN) with discontinuous activation functions and time delays is investigated by using Lyapunov stability theory. Based on linear matrix inequalities (LMIs), we originally propose robust fuzzy control to guarantee the global robust asymptotical stability of TSFNNs. Compared with the existing literature, this paper removes the assumptions on the neuron activations such as Lipschitz conditions, bounded, monotonic increasing property or the right-limit value is bigger than the left one at the discontinuous point. Thus, the results are more general and wider. Finally, two numerical examples ara given to show the effectiveness of the proposed stability results.