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\chapter{Investigation of a Non-minimal Plant Structure}  In the following a system with a non-minimal structure (shown in illustration figure  \ref{fig:plant}), i.e. zero-pole-cancellation is allowed, will be analyzed and discussed. The parameters $k,a \in \R^1$ and $\theta_u, \theta_y \in \R^{n-1}$ of the plant are to be determined in case of adaptive control.