(untitled) (PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE KYRGYZ REPUBLIC, 2025)
The frequency and algebraic directions of robust stability research are considered. The frequency or Tsypkin-Polyak direction is considered briefly in an overview manner. The algebraic or Kharitonov direction is considered more broadly, namely, the main provisions and results of the Algebraic method of robust stability of interval dynamic systems developed within the framework of the development of the algebraic - Kharitonov direction of robust stability are presented. In the author’s works, a theorem of the type of the third Kharitonov theorem is proved. For the discrete case, a discrete analog of Kharitonov’s theorem is presented, which is obtained on the basis of Schur’s theorem. At the same time, the concepts of points and intervals of intermittency used for the theorem of the analogue of the continuous case are introduced. An algorithm for determining the robustness of discrete systems is formulated.