Optimal Stabilization in Systems of Linear Differential Equations

This article considers the optimal stabilization problems for complex dynamical systems, which can be described in terms of linear differential equations. At the beginning of the article, general provisions on optimal stabilization and the application of the apparatus of optimal Lyapunov functions f...

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Bibliographic Details
Published in:	Journal of optimization, differential equations and their applications (Online) Vol. 32; no. 1; pp. 84 - 96
Main Authors:	Khusainov, Denys Ya, Diblik, Josef, Shatyrko, Andriy V., Hahurin, Zhenya R.
Format:	Journal Article
Language:	English
Published:	Oles Honchar Dnipro National University 01-06-2024
Subjects:	control lyapunov functions method stability stabilization
Online Access:	Get full text
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Summary:	This article considers the optimal stabilization problems for complex dynamical systems, which can be described in terms of linear differential equations. At the beginning of the article, general provisions on optimal stabilization and the application of the apparatus of optimal Lyapunov functions for the purpose of solving the formulated problem are given. To ensure consistency and easier understanding of the obtained results, the systems with scalar control are considered first. The main results were obtained for systems with n-dimensional control and the presence of a diagonal matrix in the quality criteria. Finally, the conditions are extended to the case when a matrix of the general form is used in the quality criterion
ISSN:	2617-0108 2663-6824
DOI:	10.15421/142405