The phrase "entirely controlled" is correct and usable in written English.
You would use it to indicate that something is completely under another's control, such as in the sentence "The production process was entirely controlled by the project manager."
Sadly, he suffered from mental illness on and off, and diabetes, which he never entirely controlled.
By 1890, the native population had been decimated by disease and the land was almost entirely controlled by haoles (foreigners).
In the absence of a properly organised book market, many countries may well switch to an all-digital market entirely controlled by the giants of the internet age.
The media is entirely controlled by the military, and 2,100 political activists who might otherwise take part in the elections are in jail.
Perhaps the most complicated dimension of all this is that construction jobs on city projects in a union town are not entirely controlled by the contractors.
Primarily small shopkeepers and traders, the new immigrants migrated westward, founding new Jewish centres that were almost entirely controlled by laymen.
His comments represented some of his harshest criticism of a state government entirely controlled by fellow Democrats, some of whom are under investigation by his own office.
Then comes a remorseless feeling that one's livelihood, and everything on which it depends, could be entirely controlled by someone who has no interest in your welfare and cares only to better their own position.
The spacing of trains, their speeds and when they start and stop will be entirely controlled by a complicated system of onboard and remote computers that communicate with each other via radio signals.
This can be a tough town, with tough crowds, as Chávez may have learned in appearances at the United Nations, during which he has not entirely controlled his own impulses.
