“…Phenomenological models, on the other hand, are used to produce behaviors similar to those of physical systems without necessarily providing physical insight into the problems. A popular phenomenological hysteresis model adopted for smart materials is the Preisach model (Adly, Mayergoyz & Bergqvis, 1991;Hughes & Wen, 1994;Ge & Jouaneh, 1996;Gorbet, Wang, & Morris, 1998;Cruz-Hernandez & Hayward, 2001;Tan, Venkataraman, & Krishnaprasad, 2001;Natale, Velardi, & Visone, 2001;Croft, Shed, & Devasia, 2001), where the hysteresis is modeled as a (weighted) aggregate e ect of all possible delayed relay elements. A similar operator using delayed relays of ÿnite slopes, called Krasnosel'skii -Pokrovskii (KP) operator, has also been used ( Banks, Kurdila, & Webb, 1997;Galinaitis & Rogers, 1998).…”