In this paper, we consider the optimal simultaneous stabilization problem for a collection of linear time-invariant descriptor systems. The objective function for the collection of systems is defined to be the sum of all quadratic objective functions associated with individual systems. The problem is to choose an output feedback gain such that the objective function is minimized. Firstly, the set of all the output feedback gains for which the objective function is finite is characterized and proven to be a compact set. Secondly, an iterative algorithm based on the gradient flow idea is derived for solving this problem and some properties on the gradient flow are obtained to guarantee the success of this method. Thirdly, an initial value for the gradient flow equation is found by solving a standard unconstrained optimization problem. Finally, two numerical examples are solved for illustration.