On the geometric structures of the H∞ controllers for descriptor systems

In this paper, we explore the geometric structures of the H∞ central controllers for descriptor systems based on the notions of deflating subspaces for singular matrix pencil. A reduced order H∞ controller is given based on the geometric structures addressed in this paper. The geometric connection between the plant and the H∞ 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.