This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.