A design method of a nonlinear vibration controller for smart piezoelectric structures is proposed based on resetting differential equations. A nonlinear vibration controller which fulfils the Lyapunov stability is worked out by emulating the effect of the switching system with piezoelectric shunt damping. A dynamical model of the plant and the control algorithm of the controller are developed, the inductor, the resistor and the switching action in the emulated circuit only "exist" as numerical representations inside the controller. The controller overcomes the disadvantages of the passive piezoelectric shunt damping technique, eliminates the need for a large physical inductor and has less sensitive to environmental changes. The simulation results for a cantilever beam show that the controller can suppress the structural vibration of controlled mode effectively and also has a certain contribution to vibration suppression for the other modes.