Sensitivity of a class of dynamic systems with respect to a small delay

In feedback loops of dimensionally large systems the signal propagation time c around the loop may become non-negligible compared to the inverse of the loop bandwidth. Such a situation exists, for example, in several particle accelerators, which use feedback to control some dynamic properties of the particle beam in the accelerator ring. The length of connecting cables may run into hundreds of metres, which leads to a delay of several microseconds, the loop bandwidth being of the order of 50 kHz. The analysis of a dimensionally large feedback loop is given. (31 refs).