The notion of system in control theory and control relatives (Q1904433)

The author first reviews the four axioms of a control system as provided by \textit{E. Sontag} [Mathematical control theory, Springer, New York (1990; Zbl 0703.93001)]. Sontag's axioms are broad enough to describe control systems which are not necessarily described through a system of differential or difference equations. In order to achieve an algebraization the author argues that an additional fifth axiom (which he calls `reduction axiom') would be helpful. This axiom essentially states that different input variables result in different state behaviors. The main result of this paper is a bijective correspondence between the classes of control systems satisfying all five axioms and a set of so called `control relatives' (German: Regel-Relative).