Geodesic
Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov — Krasovskii and Razumikhin approaches
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 198-208
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The nonlinear time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov — Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.
Keywords: time-delay systems, asymptotic stability, asymptotic quiescent position, Lyapunov — Krasovskii functionals. 
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S. E. Kuptsova; S. Yu. Kuptsov. Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov — Krasovskii and Razumikhin approaches. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 198-208. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a0/

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