Article IV, Section 2 of the U.S. Constitution states, “The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature can-not be convened) against domestic Violence.”
This provision, known as the guarantee clause, is attributed to James Madison. It has not been widely interpreted, but scholars think it ensures that each state be run as a representative democracy, as opposed to a monarchy (run by a king or queen) or a dictatorship (where one individual or group of individuals controls the government). Courts however have been reluctant to specify what exactly a republican form of government means, leaving that decision exclusively to Congress.
www.justicelearning.org, The United States Constitution, what it says, what it means, A Hip Pocket Guide (Oxford University Press)