What countries have controlled Algeria, Morocco and Libya?

Algeria : the Carthaginians, Romans, and Vandals. The region was conquered by the Muslims in the early 8th century AD, but broke off from the Umayyad Caliphate after the Berber Revolt of 740. Later, various Berbers, Arabs, Persian Muslim states, Sunni, Shia or Ibadi communities were established that ruled parts of modern-day of Algeria: including the Rustamids, Ifranids, Fatimids, Maghrawas, Zirids, Hammadids, Almoravid, Almohads, Hafsids, and Ziyyanids., and french, Ottoman

The recorded history of Morocco begins with the Phoenician colonization of the Moroccan coast between the 8th and 6th centuries BCE,[3] although the area was inhabited by indigenous Berbers for some two thousand years before that. In the 5th century BCE, the city-state of Carthage extended its hegemony over the coastal areas.[4] They remained there until the late 3rd century BCE,[5] while the hinterland was ruled by indigenous monarchs.[4] Indigenous Berber monarchs ruled the territory from the 3rd century BCE until 40 CE, when it was annexed to the Roman Empire. In the mid-5th century AD, it was overrun by Vandals, before being recovered by the Byzantine Empire in the 6th century.

The region was conquered by the Muslims in the early 8th century AD, but broke away from the Umayyad Caliphate after the Berber Revolt of 740. Half a century later, the Moroccan state was established by the Idrisid dynasty.[6][7] Under the Almoravid and the Almohad dynasties, Morocco dominated the Maghreb and Muslim Spain. The Saadi dynasty ruled the country from 1549 to 1659, followed by the Alaouites from 1667 onwards, who have since been the ruling dynasty of Morocco.

Libya: The history of Libya comprises six distinct periods: Ancient Libya, the Roman era, the Islamic era, Ottoman rule, Italian rule, and the Modern era.