This paper investigates the false data injection (FDI) attack dynamic reconstitution and se-cure control problems for cyber-physical systems (CPSs) with disturbances. The FDI attacks on the actuator channel and sensor channel are considered simultaneously, and the attack signals acting on the system side are regarded as time-varying signals. Firstly, a novel ad-justable proportional-integral multivariable observer (APIMO) scheme is designed to syn-chronously reconstitute the system states, actuator FDI attacks, and sensor FDI attacks. In particular, the impacts of instantaneous increment of attack signals are attenuated, which enables the proposed APIMO scheme more advantageous in reconstituting time-varying attack signals. Secondly, incorporating a robust attenuation technique, an APIMO-based se-curity controller with corrective capability is designed, such that the discrete-time CPSs achieve asymptotic stability with H infinity performance index. Finally, the simulation example and experiment compared with existing results are realized to examine the feasibility and advantages of the developed strategy.