線形フィードバックの well-posedness の特徴づけ

抄録

This paper presents preliminary results of a linear feedback theory in the framework of the mathematical general systems theory. The concept of basic linear systems is introduced as an abstract model of linear dynamical systems. In order to establish a feedback theory in the framework of basic linear systems, the following fundamental questions are to be answered:
(1) Does a feedback system, exist?
(2) If it exists, does it also belong to the class of basic linear systems?
In this paper, in order to discuss the “state feedback”, state systems (which form an important subclass of basic linear systems) are considered and after defining the above questions as a well-posedness problem the following results are given:
(i) A necessary and sufficient condition for the existence of a feedback solution is specified.
(ii) The class of state systems with the above condition is proved closed under the feedback transformation. In other words, the problem of this class is well-posed.