The Islamic states that you are referring to here are the Ottoman, the Safavid, and the Mughal empires.  All of these empires were in some ways successor states of the Mongol Empire carved out by Genghis Khan.  As such, these empires were all affected by the steppe traditions of the Mongols.  However, when imperial powers conquer new areas, they also tend to be influenced by the areas which they conquer.

One of the major examples of steppe influences on these empires was the idea that their rulers should have autocratic powers.  This was true in all of these empires, influencing them to have rulers who did as they pleased.  Steppe traditions also made succession more difficult.  In the steppes, the ruler’s relatives were typically given positions of power.  This led to a situation where family members would compete for supreme power upon the death of the ruler. 

These empires were also affected by the regions which they conquered.  Perhaps the biggest influence was that of Islam.  These Islamic states only became Muslim because of the influence of the areas they conquered.  This influence caused them to become dominated by Islam even though they had originally come from Mongol, non-Islamic origins.