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## Robust formulas for optimal H∞ controllers

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Author(s) : Peter Benner , Ralph Byers , Philip Losse , Volker Mehrmann , Hongguo Xu

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 20-2010

MSC 2000

93B36 $^\infty$-control
65F15 Eigenvalues, eigenvectors

Abstract :
We present formulas for the construction of optimal H∞ controllers that can be implemented in a numerically robust way. We base the formulas on the γ-iteration developed in [6]. The controller formulas proposed here avoid the solution of algebraic Riccati equations with their problematic matrix inverses and matrix products. They are also applicable in the neighborhood of the optimal γ, where the classical formulas may call for the inverse of singular or ill-conditioned matrices. The advantages of the new formulas are demonstrated by several numerical examples.

Keywords : H∞ control, controller design, optimal controller, CS decomposition, Lagrangian subspaces, even pencil

Notes :
Preprint submitted to Automatica