Geodesic
Classes of linear approximations providing various types of stability or instability of differential systems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2023), pp. 8-15

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Relationships (inclusions, coincidences, non-coincidences) 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 are studied. A complete set of non-coinciding stability classes is presented and some considerations are given for a similar description of instability classes. 
@article{VMUMM_2023_4_a1,
     author = {I. N. Sergeev},
     title = {Classes of linear approximations providing various types of stability or instability of differential systems},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--15},
     publisher = {mathdoc},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a1/}
}
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I. N. Sergeev. Classes of linear approximations providing various types of stability or instability of differential systems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2023), pp. 8-15. http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a1/