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

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... e 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.