Abstract. In this paper we consider the mathematical model of hysteretic damper based on the IshlinskyPrandtl model. The numerical results for the observable characteristics such as force transmission function and "force-displacement" transmission function are obtained and analyzed. The comparison of the efficiency of nonlinear viscous damper and hysteretic damper is also presented and discussed.

Abstract. In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of backlash) under state feedback control. The analytic results for the stability criteria as well as for the solution of the linearized equation are observed and analyzed. The theorems that determine the stabilization of the considered system are also formulated and discussed.