Preservation of controllability under approximation and controllability radii for hereditary systems (Q752611)

The main goal is to point out several difficulties associated with the preservation of system properties under approximation. In order to illustrate the basic problems, we concentrate on the relationship between controllability properties of an infinite dimensional system and its finite dimensional approximations. In particular, we consider the question of preservation of controllability for a distributed parameter system governed by a simple delay-differential equation and approximated by using several computational schemes. Even this rather ``simple'' class of problems leads to several interesting open questions. However, we hope that the reader is motivated by this example to consider similar problems for more complex distributed parameter systems.