Abstract: This paper focuses on the problem robust H∞ control design for affine uncertain descriptor systems in both state and input matrices. Necessary and sufficient conditions for quadratic stabilization with a H∞-norm bound are derived by a generalized algebraic Riccati inequality (GARI) with a so-called descriptor constraint. The relationship between the stabilization and the quadratic stabilization, and a design for the controller were given. The controller was obtained by the known information of the given uncertain descriptor systems. Finally, an example was given to illustrate the main results.