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Preprint 19-2012

Robust control via the computation of permuted graph bases

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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

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