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The article is devoted to the actual problem of the mathematical theory of controllability. It investigated the mathematical model of control, described by ordinary differential equations, taking into account the restrictions on the control. As is known, the problem of finding controllability of dynamic systems with phase and control constraints is still relevant. There are many approaches to solving the determined problem. The classical control theory is being modified today and it finds new methods for solving problems of controllability, optimal control and stability, the solutions obtained. In the course of studying the controllability of a dynamic system, the authors applied interval mathematics, which made it possible to obtain an effective controllability criterion for dynamic systems with phase and control constraints. This method is applicable for a certain class of problems in which the data are described by the normal distribution law. The constructiveness of the proposed criterion is demonstrated in two examples. The first is a model problem described by 2-nd order equations. The second is an electromechanical tracking system of an automatic manipulator, described by equations of the 3rd order. Thus, for dynamic systems, we obtained a sufficient condition for controllability.

The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard-Shipar interval criteria. Krylov, Leverier, and Leverier-Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems.