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Interpretations of most existing controllability and observability notions for linear delay systems are given. Module theoretic
characterizations are presented. This setting enables a clear and precise comparison of the various examined notions. A new notion of
controllability is introduced, which is called pi-freeness.
A vibrating string, modelled by the wave equation, with an interior mass is considered. It is viewed as a linear delay system. A trajectory tracking problem is solved using a new type of controllability.
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