Feedbacks for non-autonomous regular linear systems

We introduce non-autonomous well-posed and (absolutely) regular linear systems as quadrupels consisting of an evolution family and output, input and input-output maps subject to natural hypotheses. In the spirit of G. Weiss´ work these maps are represented in terms of admissible observation and control operators (the latter in an approximative sense) in the time domain. In this setting the closed-loop system exists for a canonical class of ‘admissible’ feedbacks, and it inherits the absolute regularity and other properties of the given system. In particular, one can iterate feedbacks.