Absorption of electromagnetic waves by graphenemagnetic semiconductor multilayered structure has been investigated for the Voight geometry with taking into account the dissipation processes. The possibility of control of electrodynamic properties of the structure by an external magnetic eld, changing in number of periods of the structure, chemical potential of the graphene layers and temperature has been shown. Electrodynamics of the structure is also sensitive to polarization of the incident wave. The structure shows to be especially controllable at terahertz frequencies.