Two recent results on earthquake control are summarized in this conference presentation, with emphasis on sliding mode control. A simplified model of an earthquake instability is addressed by means of a cascade system of a 1D wave equation, representing the fault slip and wave propagation, and a 1D diffusion equation, representing the injection of fluid as a diffusion process. In order to avoid a fast slip (earthquake-like behavior), the control is designed to follow a slow reference in both systems despite model uncertainties and perturbations. Simulations are additionally conducted to support the robustness and stability properties of the proposed control algorithms, by separately, obtaining critical remarks that will lead to the design of the single control for the cascade system in a future stage.