Smooth model of the relay with hysteresis

A model of the relay with hysteresis following the ordinary differential equation with large parameter was proposed. It offers a convenient vehicle for numerical analysis using the advanced packages of the applied programs and also may prove helpful in the qualitative studies of the control systems with the methods of the differential equation theory. Consideration was given to the question of the smooth model error as compared with the existing discrete models. The main result lies in the fact that for a certain class of the relay control systems the behavior of such systems with smooth model having the parameter tending to infinity converges uniformly over any time interval to the corresponding behavior of systems with discrete model. Closeness of these kinds of behavior was estimated, and a special case was discussed.

Presented by the member of Editorial Board: A. M. Krasnosel'skii