This paper deals with observer-based forms of arbitrary continuous-time descriptor controllers. The general form includes static control and estimation gains with or without an extra descriptor Youla parameter that can be either static or dynamic. A necessary and sufficient condition for the derived controller to be input-output equivalent to the initial one, with a separated estimation-control structure, is given. The present method is consistent with the existing results in the conventional linear state-space case. Some numerical examples illustrate the effectiveness of the proposed method.