On stability and stabilization of motion with respect to a part of the variables
type: Item
instance of: scholarly article
title: On stability and stabilization of motion with respect to a part of the variables
zbMATH Open document ID: 0539.93061
DOI: 10.1016/0021-8928(82)90053-3
author: V. I. Vorotnikov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1983-01-01T00:00:00Z
review text: The comparison method, in case of Ljapunov vector functions, is applied in the investigation of partial stability of the motion of a system described by ordinary differential equations with continuous right-hand sides. A technique is developed which enables to solve the partial stabilization problem under certain requirements regarding the nature of transition processes of the system. To illustrate the applicability of the obtained results six examples are considered and solved. Finally, one discusses a technique and a method, both derived from the main results, which enable to solve partially the problem of minimizing the demand on resources and, respectively, to solve a functional minimization problem and a game theoretic problem on a minimax-maximin of a functional, with the scope of satisfying certain requirements regarding the transition processes with respect to a part of the variables.
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 91A99
Mathematics Subject Classification ID: 70K20
zbMATH DE Number: 3858980
zbMATH Keywords: comparison method
zbMATH Keywords: Ljapunov vector functions
zbMATH Keywords: partial stability
zbMATH Keywords: functional minimization
zbMATH Keywords: minimax-maximin
reviewed by: Mihail Voicu
MaRDI profile type: Publication
full work available at URL: 0021-8928(82)90053-3
OpenAlex ID: W2052717217
cites work: The method of Ljapunov functions in the stability problem for motion with respect to a part of the variables
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description: scientific article; zbMATH DE number 3858980