Modelling physical hysteresis and control of a fine piezo-drive

New universal and constructible approach for mathematical description of physical hysteresis is presented. This approach is based on using set-valued differential equation with discontinuous right-side and on a shape parameterization of a hysteresis relation. Developed approach is efficiently applied for nonlinear dynamic research of the fine piezo-ceramic micro-drive for an image motion stabilization at a space Earth observing telescope.