Mathematics & Physics 2016, 9(4), 498–509 УДК 51-74, 517.9, 531.536 State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension Mikhail E.Semenov∗ Zhukovsky–Gagarin Air Force Academy, Starykh Bolshevikov, 54-A, Voronezh, 394064 Voronezh State University, Universitetskaya, 1, Voronezh, 394006 Voronezh State University of Architecture and Civil Engineering XX-letiya Oktyabrya, 84, Voronezh, 394006 Russia Zainib Hatif Abbas† Voronezh State University of Architecture and Civil Engineering XX-letiya Oktyabrya st. 84, Voronezh, 394006 Russia Igor N. Ishchuk‡ Zhukovsky–Gagarin Air Force Academy, Starykh Bolshevikov, 54-A, Voronezh, 394064 Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041 Russia Olesya I. Kanishcheva§ Zhukovsky–Gagarin Air Force Academy, Starykh Bolshevikov, 54-A, Voronezh, 394064 Voronezh State University of Architecture and Civil Engineering XX-letiya Oktyabrya, 84, Voronezh, 394006 Russia Peter A. Meleshenko¶ Zhukovsky–Gagarin Air Force Academy, Starykh Bolshevikov, 54-A, Voronezh, 394064 Voronezh State University, Universitetskaya, 1, Voronezh, 394006 Russia Received 27.04.2016, received in revised form 20.06.2016, accepted 15.08.2016 In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of a 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 formulated and discussed. <...> The question on the optimal control of the system under consideration is also discussed and the corresponding theorem is considered. <...> All rights reserved c – 498 – Mikhail E.Semenov, Zainib Hatif Abbas . . . <...> State-feedback Control Principles for Inverted Pendulum . . . <...> Typical examples are feedback stabilization, variable structure control, passivity based control , back-stepping and forwarding, nonlinear observers, friction compensation, and nonlinear model reduction. <...> In order to make an adequately description of the dynamics of real physical and mechanical systems it is necessary to take into account the effects of hysteretic nature such as "backlash", ‘"tops" etc. [14]. <...> The mathematical models of such nonlinearities according <...>