Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 3, pp. 326-340   https://doi.org/10.15407/mag17.03.326     ( to contents , go back )
https://doi.org/10.15407/mag17.03.326

The Peculiarity of Solving the Synthesis Problem for Linear Systems to a Non-Equilibrium Point

Valeriy Korobov

V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine
E-mail: vkorobov@univer.kharkov.ua

Kateryna Stiepanova

Simon Kuznets Kharkiv National University of Economics, 9a Science Ave., Kharkiv, 61166, Ukraine

V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine
E-mail: e.v.stiepanova@gmail.com

Received November 9, 2020.

Abstract

The paper is devoted to the problem of the construction of a control which transfers a control system from any point to a given non-equilibrium point in a finite time. The construction of the control is based on the method of controllability function. The ambiguity of the solution of the equation that determines the controllability function is found, which leads to a number of interesting cases. The problem is solved for a linear system. The obtained results are illustrated on a model example.

Mathematics Subject Classification 2010: 93B05, 93B11, 93C10
Key words: controllability function method, linear system, non-equilibrium point

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