Iranica is not the only source. Minorsky said:

 By that time the great Seljuks were gone and their epigoni were eclipsed by their former vassals. The latter, when united, represented a serious force, but the Georgians, with their allies and vassals from Northern Caucasus (the Qipchaq Turks), could cope with any ephemeral coalitions. Only with the rise of the atabeks of Azarbayjan (the Eldiguzids) was a brake put on the Georgian expansion in two directions: to the South-towards the Armenian lands deprived of their independence by the Muslims; and to the East-towards the Caspian sea. It is true that the rulers of Shirvan had been linked to the Georgians by family ties; but Ganja,2 on the Georgians' right flank, formed a brake on the forward policy of the Christian kings. 

 The article in Iranica also says that Atabeks controlled Ani, which is in Turkey. So clearly Atabeks controlled larger area, which included the territory of modern day Azerbaijan (both independent and Iranian), Armenia and part of Turkey.