The phrase "able to assert their" is correct and usable in written English.
It can be used when discussing someone's capability to express or declare something confidently or forcefully.
Example: "The students were finally able to assert their opinions during the debate."
Alternatives: "capable of expressing their" or "able to declare their".
How will a parent in an abusive relationship be able to assert their independence if their partner controls the income?
No longer able to assert their masculinity as much through their gender, straight men turned to sexuality.
Then, during Obama's tenure, senators were yet again able to assert their power to block judicial nominees.
"The government obviously wants to keep its cooperators safe, and other people want to be able to assert their claims in court," he said.
With Assad and the main rebel forces consumed with fighting each other, it appears unlikely that either will be able to assert their authority over the north-east.
As 20% of a new Ireland, unionists will be able to assert their full rights and entitlements and exercise real political power and influence.
So long as independent directors are able and willing to assert their independent judgment, there is nothing wrong with directors and management developing relationships of mutual respect, trust and friendship.
But the United States is also an area where Mexicans forgotten in Mexico have been able to assert themselves with their own unique cuisine, frequently finding fans among Americans unlike in Mexico, where their culinary treasures wouldn't have been able to get them arrested.
In Aquitaine, of which the counts of Poitiers were dukes, and in the county of Toulouse the viscounts were great barons often able to assert themselves against their suzerain.
Leaders must be able to assert themselves and their agenda.
Although the level of empowerment of the Mitanins was much higher than that of other women, nonetheless, many women were able to assert themselves both within their family and in the community.
