Contents I. Introduction
The problem of control of an inverted pendulum on a mobile cart [1] is one of the classical problems. It is used often as an example, on the base of which the results of modern research on control theory are demonstrated. Despite the huge number of publications devoted to this problem, a number of unexplored issues remain. The main problem concerned with the control of an inverted pendulum on a cart is the substantial nonlinearity of the system under consideration. There are a number of approaches based on the theory of sliding modes [2], systems with separated motions [3], [4], the theory of dissipative systems [5], etc. It is necessary to note, that in the described publications not enough attention is paid to the implementation of these approaches in practice, when additionally with the equations of the mechanical subsystem, the dynamic subsystem describing the behaviour of actuators is considered also.
