The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state feedback and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of two Hamilton-Jacobi inequalities and a weak coupling condition; a parameterization of a family of output feedback controllers solving...