I am reading Wael Hallaq's An Introduction to Islamic Law (Cambridge 2009, 170 pp., plus a useful glossary). This is a short and very readable history of the development of Shari'a from the late seventh century on.
In pre-modern Islam they focused on the idea of a "Circle of Justice." Here is Hallaq's description:
The notion of a Circle of Justice begins with the idea that no political sovereignty can be attained without the military; yet no military can be sustained without financial resources. These resources furthermore can be raised only through levying taxes, which presupposes continuous economic productivity on the part of the subjects; but to maintain a level of prosperity that can sustain taxable income, justice needs to be ensured, and this in part means controlling the excesses of provincial officials whose vision of justice may be overshadowed by personal power and rapacity. Thus, to be attained justice requires public order, all-important social harmony, and control of abusive and greedy government servants. To achieve all this, the Shari'a, clearly the axis of governance, points the way. But the Shari'a cannot be implemented without political sovereignty, and this cannot be attained without the military. Here, Circle is joined.The Wikipedia entry for "Ottoman Empire Circle of Justice" claims that this bears a striking resemblance to European feudalism. But that's wrong. The virtuous Circle of Justice sounds notably more modern to me. In a modern liberal democracy we would replace "Shari'a points the way" with "the Law points the way," by which we mean law that enshrines Enlightenment values, individual rights, a free press, freedom of speech and conscience, and a a well regulated economy. But otherwise, all aspects of this circle in the diagram above apply today.
Feudalism is a concept of land tenancy between nobles and vassals. The Circle of Justice as described here does not address land tenancy at all. Moreover, the classic feudal era in Europe was marked by the crazy notion of the divine right of kings, which claimed unfettered and absolute (God given) authority to the kings. The divine right of kings is a concept utterly foreign to the Shari'a as described by Wallaq. The sovereign under Shari'a derived his legitimacy from the legal scholars who interpreted the Law; the sovereign was acting as a mere trustee on behalf of God's Law, and he was answerable to the Law as interpreted by the scholars.
Pre-modern Islam was in this sense much more modern than medieval Europe.