We consider a hysteresis operator that arises as a three state generalization of a bi-stable relay. Basic properties and a geometric interpretation of the three-state relay are considered. Analogously to Preisach operator, which
can be introduced as an aggregation of all possible non-ideal relays, we consider a "Super-Preisach" operator, that is an aggregation of all possible three-state relays.
Mathematics Subject Classification: Primary: 34C55; Secondary: 47H99.