The phrase "asserted influence" is correct and usable in written English.
It can be used when discussing the influence that someone claims to have or has stated they possess in a particular context.
Example: "The researcher asserted influence over the study's outcomes, claiming that their expertise shaped the results."
Alternatives: "claimed influence" or "exerted influence".
Europe and the United States are asserting influence through N.G.O.'s and by backing political changes.
Moiré patterns, TV color bars, musical structures, and rules-based composition assert influence, as do performance and, undeniably, sculpture.
Dastyari has done us all a favour by highlighting one problem in the current system: the capacity for foreign interests to try and assert influence in our democracy.
"Successful political operatives," Mr. Strauss said, "are in the main people who are able to contain their desire for visibility and assert influence behind the scenes".
But they say Shiite Muslim militias, some with close ties to Iran, also appear to be conducting some of the killings to assert influence and settle scores.
He said Iran's action had more to do with sending a message to Washington and asserting influence as a regional power than with achieving a new military capability.
A Times report published last weekend, about Jeb's many notes and requests to the White House on other matters when his father worked there, suggests that he "normally" wasn't shy at all about asserting influence inappropriately.
Still, the effort to squeeze the dollar out of Russian oil sales is yet another project notable for swagger and ambition by the Kremlin, which has already wielded its energy wealth to assert influence in Eastern Europe and former Soviet states.
He has wielded Gazprom as a blunt weapon against Ukraine, where corruption has provided the company with rich opportunities to assert influence and to manipulate huge amounts of cash.
