Abstract: The solvability of quadratic matrix inequalities of singular H∞ control problems with infinite zeros is studied in this paper. It is proved that the quadratic matrix inequality can be solved directly via the generalized eigenvalue problems. The previous method of solving the quadratic matrix inequality involving complicated decompositions and transformations of the systems is avoided. The connection between two different approaches to singular H∞ control problems based on geometric control theory and (J,J')-lossless factorization theory respectively is established. This paper illustrates the eigenspace structure of singular H∞ control systems.