Stability of Difference Analogue of Linear Mathematical Inverted Pendulum

To use numerical investigation of functional differential equations it is very important to know if difference analogues of the considered differential equations have the reliability to preserve some general properties of these equations, in particular, property of stability. This problem is considered here by investigation of a difference analogue of the linear mathematical inverted pendulum. The problem of stabilization of the mathematical inverted pendulum is very popular among the researches (see, for instance [1, 2, 3, 5, 13, 14]). The linearized mathematical model of the controlled inverted pendulum can be described by the following linear differential equation of second order