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Preprint 08-2005

Evaluation of Numerical Methods for Discrete-Time H-infinity Optimization

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Author(s) : Volker Mehrmann , Petko Petkov

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 08-2005

MSC 2000

93C55 Discrete-time systems
93D09 Robust stability

Abstract :
We compare the numerical properties of the different numerical methods for solving the H-infinity optimization problems for linear discrete-time systems. It is shown that the methods based on the solution of the associated discrete-time algebraic Riccati equation may be unstable due to an unnecessary increase in the condition number and that they have restricted application for ill-conditioned and singular problems. The experiments confirm that the numerical solution methods that are based on the solution of a Linear Matrix Inequality (LMI) are a much more reliable although much more expensive numerical technique for solving H-infinity optimization problems. Directions for developing high-performance software for H-infinity optimization are discussed.

Keywords : H-infinity-optimization, H-infinity-control, discrete-time system,linear matrix inequality, discrete-time algebraic Riccati equation

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