The system has a dielectric barrier discharge lamp (2) with a discharge vessel (9) that is elongated in a form of a tube and contacts. The contacts are fitted at an end of the vessel for electrically connecting the lamp. A plug connection unit is connected to a housing of ballast. The plug connection unit is designed such that the lamp is connected to electronic ballast utilizing the contacts of the discharge vessel. An INDEPENDANT CLAIM is also included for a method for connecting a discharge lamp of the illumination system.