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Porovnání H-nekonečno a LQG regulace / Comparison of H-infinity and LQG controllerFriml, Dominik January 2020 (has links)
This thesis deals with the MIMO system analysis, with a comparison of a different frequency charactersitics, and including singular values characteristic. The H2 and H norms are defined for signals and a MIMO systems. A MIMO optimal control using an LQG, an H2 and an H control is defined and described. Their general advantages, disadvantages and similarities are summed up. An H2 and an H state controller and state observer synthesis is implemented in a MATLAB using linear matrix inequalities. Control of an inverted pendulum is designed using the H optimal cascade control, the H2 state control and the H state control. The results are compared with each other. The theoretical possibility of same H2 and H optimal state controller design is presented.
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The condition number of Vandermonde matrices and its application to the stability analysis of a subspace method / Die Konditionzahl von Vandermondematrizen und ihre Anwendung für die Stabilitätsanalyse einer UnterraummethodeNagel, Dominik 19 March 2021 (has links)
This thesis consists of two main parts. First of all, the condition number of rectangular Vandermonde matrices with nodes on the complex unit circle is studied. The first time quantitative bounds for the extreme singular values are proven in the multivariate setting and when nodes of the Vandermonde matrix form clusters. In the second part, an optimized presentation of the deterministic stability analysis of the subspace method ESPRIT is given and results from the first part are applied.
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