The nineteenth-century economic decline of the islamic empires can be attributed to

Isolation--follow a long period of isolation, the Islamic Empires had not been trading or gaining new innovations during the 19th century. 

As European countries began to explore and open trade, the Muslim Empires had been at their peak and refused trading rights with them. This economic isolation led the countries to also lose out on new knowledge and innovations. The Muslim Empires found themselves behind by the 20th century and unable to protect their empires.