Abstract:
We study the exponential stability of a nonlinear system of differential equations with constant delay such that the right-hand side of one of its subsystems contains the multiplier et. We obtain a sufficient condition for the first-approximation stability of this system.
Keywords:
instability, asymptotic stability, exponential estimation, first approximation.
Citation:
B. G. Grebenshchikov, “The first-approximation stability of a nonstationary system with delay”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 2, 34–42; Russian Math. (Iz. VUZ), 56:2 (2012), 29–36
This publication is cited in the following 9 articles:
B. G. Grebenschikov, S. A. Zagrebina, “Metody issledovaniya nekotorykh sistem s lineinym zapazdyvaniem”, Materialy 5 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya»
(DYSC 2023). Irkutsk, 18-23 sentyabrya 2023 g., Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 234, VINITI RAN, M., 2024, 133–142
B. G. Grebenshchikov, A. B. Lozhnikov, “On the problem of choice of methods for stabilizing systems containing linear delay”, Russian Math. (Iz. VUZ), 67:1 (2023), 30–42
B. G. Grebenshchikov, A. B. Lozhnikov, “Asymptotic Properties of a Class of Systems with Linear Delay”, Diff Equat, 59:5 (2023), 577
B. G. Grebenshchikov, “Asimptoticheskie svoistva nekotorykh sistem neitralnogo tipa s lineinym zapazdyvaniem”, J. Comp. Eng. Math., 10:4 (2023), 26–39
B. G. Grebenschikov, “Asimptoticheskie svoistva i stabilizatsiya odnoi sistemy neitralnogo tipa s postoyannym zapazdyvaniem”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 17:1 (2021), 81–96
B. G. Grebenshchikov, A. B. Lozhnikov, “Stabilizatsiya odnoi sistemy s lineinym zapazdyvaniem”, J. Comp. Eng. Math., 8:3 (2021), 3–13
Grebenshchikov B.G., Lozhnikov A.B., “Stabilization of Some Systems With Constant Delay”, IFAC PAPERSONLINE, 51:32 (2018), 105–109
B. G. Grebenshchikov, A. B. Lozhnikov, “Stability and stabilization of one class of linear nonstationary constant-delay systems”, J. Comput. Syst. Sci. Int., 56:2 (2017), 173–185
B. G. Grebenshchikov, “The asymptotic stability of a nonstationary system with delay”, Russian Math. (Iz. VUZ), 57:8 (2013), 20–28
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