Regular linear systems with feedback (Q1340092)

For an LTI state-space model \((A, B, C, D)\) with a static relationship \((D)\) between input and output there are some well-known restrictions about the admissibility of the output feedback law. The aim of this paper is to extend the above elementary results to infinite-dimensional linear systems. The class of systems considered are the regular linear systems, representable by state-space equations where \(A\), \(B\), and \(C\) are possibly unbounded operators and \(D\) is bounded. A useful section of this paper recalls the most important properties of regular linear systems. It is shown that the closed-loop system obtained from a regular linear system with an admissible feedback operator is still regular. The relationship between the open-loop and the closed-loop models is investigated.