Geodesic
Spectral Test for Exponential Stability
Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 489-498.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using the theory of commutative Banach algebras, we find an estimate of the solution of a higher-order linear differential equation; from this estimate, we derive a Lyapunov asymptotic stability test for this equation. Here the results by Faedo and Kharitonov on the Hurwitz conditions for families of polynomials find a natural application. Similar statements are obtained for a system of linear differential equations.
Keywords: commutative Banach algebras, differential equations in Banach algebras, Lyapunov stability. 
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I. D. Kostrub; A. I. Perov. Spectral Test for Exponential Stability. Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 489-498. http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a1/

[1] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1968 | MR

[2] U. Rudin, Osnovy matematicheskogo analiza, Mir, M., 1975 | MR

[3] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[4] S. P. Strelkov, Vvedenie v teoriyu kolebanii, Nauka, M., 1964 | MR

[5] Yu. L. Daletskii, M. G. Krein, Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[6] A. I. Perov, I. D. Kostrub, “Differentsialnye uravneniya v banakhovykh algebrakh”, Dokl. RAN. Matem., inform., prots. upr., 491 (2020), 73–77 | DOI | Zbl

[7] B. T. Polyak, “O nekotorykh sposobakh uskoreniya skhodimosti iteratsionnykh metodov”, Zh. vychisl. matem. i matem. fiz., 4:5 (1964), 791–803 | MR | Zbl

[8] I. M. Gelfand, D. A. Raikov, G. E. Shilov, Kommutativnye normirovannye koltsa, Fizmatlit, M., 1960 | MR

[9] A. S. Pontryagin, Obyknovennye differentsialnye uravneniya, Nauka, M., 1965 | MR

[10] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1967 | MR

[11] S. Faedo, “Un nuovo problema di stabilita per le equazioni algebriche a coefficienti reali”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 7:1–2 (1953), 53–63 | MR

[12] V. L. Kharitonov, “Problema Rausa–Gurvitsa dlya semeistva polinomov i kvazipolinomov”, Matem. fizika, 1979, no. 26, 69–79 | MR

[13] A. I. Perov, “O priznakakh obratimosti i gurvitsevosti”, Funkts. analiz i ego pril., 51:4 (2017), 84–89 | DOI | Zbl

[14] A. I. Perov, I. D. Kostrub, O. I. Kleschina, E. E. Dikarev, “Absolyutnaya logarifmicheskaya norma”, Izv. vuzov. Matem., 2018, no. 4, 70–85 | Zbl