In this paper, we explore the geometric structures of the 7-6 central controllers for descriptor systems based on the notions of deflating subspaces for singular matrix pencil. A reduced order 7-6, controller is given based on the geometric structures addressed in this paper. The geometric connection between the plant and the H-infinity controllers is then studied. A numerical example is provided. In terms of the notions of deflating subspaces, all the results and proofs given are clear and simple. (C) 2018 Elsevier Ltd. All rights reserved.