After the fall of Vijayanagara, Bengaluru was captured in 1638 by the Bijapur Sultanate. Its general Ranadulla Khan was accompanied by Shahaji Bhonsle, father of Shivaji, who received the town as a jagir.
The Mughals took it in 1687 and soon sold it to Chikka Devaraja Wodeyar of Mysore for three lakh rupees. Under the Wodeyars Bengaluru became an important fortified town of the Mysore kingdom.
Further reading: Chikka Devaraja Wodeyar on Wikipedia.