"exclusive control over" is correct and usable in written English.
You can use it whenever you want to refer to a situation in which one person or entity has control over something without any other person or entity having that same control. For example: "The company now has exclusive control over the distribution of the product."
No news organization today could get away with exclusive control over vital historic testimony for so many years.
Drug companies fight hard to keep exclusive control over their newest inventions so prices and profits remain high.
The Cubs would receive exclusive control over the use of the stadium and could sell advertising and the naming rights.
When the appellate court in Manhattan granted the F.C.C.'s request to exert exclusive control over the licenses, NextWave's reorganization plan collapsed.
While the central government has exclusive control over the national army and foreign affairs, regional law is superior to national law on almost everything else.
The European commission has denounced as "false and unfounded" claims by Greece's former finance minister Yanis Varoufakis that international creditors had exclusive control over the country's tax system.
Some just want more say in how Finnmark is run, some seek exclusive control over all minerals and fisheries, a few dream of full-blown sovereignty.
"What he wants is a regime where Israel has exclusive control over security, while the Palestinians have civil responsibility for services like health and education.
Trudeau may indeed want to do right by Indigenous peoples, but the government is locked into a logic of its own: quietly maintaining exclusive control over Indigenous peoples' lands and resources.
While ceasing Minecraft development on other platforms would give Microsoft exclusive control over one of the world's biggest game brands, such a a tactic would have huge repercussions amid the game's highly vocal community.
