Final answer:
The Mali Empire controlled the trans-Saharan trade routes in Africa through a strong central authority.
Step-by-step explanation:
The state system that controlled the trans-Saharan trade routes in Africa was the Mali Empire. The Mali Empire was one of the greatest early Sudanic empires and brought together the key components that contributed to the expansion of trans-Saharan trade. The empire's rulers were Muslims and they established a strong central authority to exercise their power.