Topics in Robustness Analysis

• In this thesis, we investigate two problems in robustness analysis of uncertain systems with structured uncertainty. The first problem concerns the robust finite frequency range H2 analysis of such systems. Classical robust H2 analysis methods are based on upper bounds for the robust H2 norm of a system which are computed over the whole frequency range. These bounds can be overly conservative, and therefore, classical robust H2 analysis methods can produce misleading results for finite frequency range analysis. In the first paper in the thesis, we address this issue by providing two methods for computing upper bounds for the robust finite-frequency H2 norm of the system. These methods utilize finitefrequency Gramians and frequency partitioning to calculate upper bounds for the robust finite-frequency H2 norm of uncertain systems with structured uncertainty. We show the effectiveness of these algorithms using both theoretical and practical experiments.

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