Using permuted graph bases in H∞H∞ control

We present a new numerical method (based on the computation of deflating subspaces) for the γγ-iteration in H∞H∞ control in the extended matrix pencil formulation. We introduce a permuted graph representation of these subspaces, which avoids the known difficulties that arise when the iteration is based on the solution of algebraic Riccati equations but at the same time makes use of the special symmetry structures that are present in the problems. We use this representation to perform both the deflation of spurious ∞∞ eigenvalues of the even pencils and the implementation of the inverse-free sign iteration. We show that the new method returns accurate results and is applicable in many situations where conventional methods fail.