The phrase "asserting influence over" is correct and usable in written English.
It can be used when discussing the act of exercising power or control over someone or something.
Example: "The organization has been asserting influence over local policies to align them with its goals."
Alternatives: "exerting control over" or "wielding power over".
Some Turkish nationalists say the Orthodox Church is a wedge for Greek expansionism, that Orthodox priests are its agents and that their visits to the Black Sea region are intended to assert influence over a region they would like to control.
New Komeito questioned Mr Abe's moves last year to assert influence over the central bank's conduct of monetary policy.With his poll ratings high, Mr Abe appears to be looking at alliances with two likelier LDP bedfellows, the economically liberal Your Party and the right-wing Japan Restoration Party.
Europe and the United States are asserting influence through N.G.O.'s and by backing political changes.
The idea is that he is asserting his influence over the Dodd-Frank rule-making process.
But recently he has been trying to assert greater influence over education, and through his office, he can generate considerable public pressure on the Regents.
Mr. Poindexter, who is 65, was a controversial figure both for his role in the Iran-contra scandals and for his efforts to assert military influence over commercial computer security technologies.
Boosted by the news that the terminal ALS he was battling was, in fact, misdiagnosed, he now has a new lease of life and attempts to assert his influence over his Empire record label from inside.
Former immigration officials said that moving Mr. Cronin to oversee inspections would also let Stuart Anderson, the agency's top official for plans and policy, assert more influence over immigration programs.
But the officials said they were still sifting through intelligence reports to determine whether the attacks indeed marked an attempt by Al Qaeda to assert more influence over the Pakistani Taliban's operations.
