Controllability of dynamical systems with Play-type hysteresis via approximation by delayed relays

In this paper we study the controllability problem for systems exhibiting hysteresis represented by play-type operators. To this end we first formalize and study in a functional setting the approximation of the Play operators by a finite weighted sum of delayed relay. Then we prove the controllability for the case with the Play operator, by the controllability result for the case with the weighted sum of delayed relay. Finally, we discuss potential applications of our approach to the sweeping process.