"Controlled" should be used loosely since it was until the British and Spanish Navies of the 1700's that any nation had the ability to actually control the trade route around the southern tip of Africa, but Portuguese explorers were the first to discover it. By progressively exploring further south, each ship's captain made written maps and records that were advanced by the next explorer (they left markers on the shore to those that followed). Bartolomeau Diaz was first to discover tip and Vasco de Gama then the first to make his way around the tip to India in 1498. Through their knowledge of the route, they dominated the trade route, but by late 1500s/early 1600s others had also discovered it for themselves and were using it widely. This was still a long and difficult passageway to India which drove nations to try to find a shorter route by going west across the Atlantic and this subsequently led to discovery and exploration of North/South America by Columbus and others.
Dutch
Sunni Ali and Askia Muhammad ruled Songhai (an African kingdom) in the 1600s
The Moguls.
The Iphone 4
Some common names for French girls in the 1600s were Barbe, Gabrielle, Germaine, Laurentine, and Merci. Others included Ursuline, Silvaine, Michelle, Nicolette, and Esperance.
Europe
Brazil
If you mean as a colonial power, the Netherlands.
France controlled Algeria from the 1830s to the 1960s. Also, if you consider Turkey European, the Ottoman Empire controlled Algeria for much of the 1600s and 1700s.
Ottoman Empire
The Ottoman Empire
England was the dominant European country in the early 1600s.
In the early 1600s, the Dutch settled in New York (I'm not sure why.), and after several years, the English took over.
India
It increased because it did!
England
germany