Author(s) :
Volker Mehrmann
,
Federico Poloni
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 19-2012
MSC 2000
- 65F30 Other matrix algorithms
-
49-04 Explicit machine computation and programs
Abstract :
We present a new numerical method for the γ-iteration in robust control based on the extended matrix pencil formulation of [Benner, Byers, Mehrmann, Xu 2007]. The new method bases the γ iteration on the computation of special subspaces associated with matrix pencils. 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 show that the new method is applicable in many situations where the
conventional methods fail.
Keywords :
robust control, H-infinity control, algebraic Riccati equation, permuted graph basis, Lagrangian subspace