Exponential synchronization of discontinuous complexvalued complex dynamical network with nonlinear perturbation via feedback control and timedelayed impulsive control is studied, among which feedback control and timedelayed impulsive control are used to overcome the influence of complex dynamical network caused by discontinuous activation function. Based on the methods such as Filippov solution, differential inclusion, Lyapunov function and so on, this paper proposes some sufficient conditions to guarantee the exponential synchronization of discontinuous complex dynamical network. The results of this paper are promoted and improved by previous results and can be directly applied to the continuous complex dynamical network. Finally, numerical simulations are given to show the effectiveness of the theoretical results.