Classes of Linear Approximations Providing Different Stability or Instability Types of Differential Systems

Classes of Linear Approximations Providing Different Stability or Instability Types of Differential Systems

The paper studies relationships (inclusions, coincidences, and noncoincidences) between classes of linear approximations that provide various properties of Lyapunov, Perron, and upper-limit stability or instability (from global to particular) of the zero solution to a differential system of arbitrar...

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Bibliographic Details
Published in:Moscow University mathematics bulletin Vol. 78; no. 4; pp. 163 - 169
Main Author: Sergeev, I. N.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01-08-2023
Springer Nature B.V
Subjects:
Analysis
Approximation
Inclusions
Mathematics
Mathematics and Statistics
Stability
stability in the first approximation
upper-limit stability
Lyapunov stability
differential system
linear approximation
Perron stability
nonlinear system
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Summary:The paper studies relationships (inclusions, coincidences, and noncoincidences) between classes of linear approximations that provide various properties of Lyapunov, Perron, and upper-limit stability or instability (from global to particular) of the zero solution to a differential system of arbitrary order. A complete set of noncoinciding stability classes is presented and some considerations are given for a similar description of instability classes.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132223040083