Stability without eigenspaces in the geometric approach: The regulator problem

The regulator problem with the plant stability condition is investigated by using new tools of the geometric approach, i.e., self-bounded controlled and self-hidden conditioned invariants, recently introduced by the authors. In this framework, a constructive procedure which solves the problem without eigenspaces is obtained. This procedure also includes a set of necessary and sufficient conditions which, compared with those previously known in the literature, are significantly simpler in their statement and more easily mechanized.This research was supported by the Italian Ministry of Education. This paper is an extended version of a communication presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems, Phoenix, Arizona, 1987.