A necessary optimality condition for the linear-quadratic DAE control problem

We consider the linear-quadratic optimal control problem for a controlled differential algebraic equation (DAE). Under minimal assumptions on the DAE concerning index and regularity it will be possible to prove that the sufficient optimality condition given in papers of G.Kurina and R.März is also a necessary condition. This condition includes the solution of an appropriate boundary value problem and, in the special case of an explicit ordinary differential equation, the condition is equal to the well known necessary and sufficient condition of the classical linear-quadratic optimal control problem