Geodesic
Application of quadratic Lyapunov functions to investigation of stability of systems with delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 15-20.

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The particular attention when studying delay systems is payed to such important systems property as its stability. When studying ordinary differential systems stability by Lyapunov functions method quadratic Lyapunov functions are widely used. This paper is devoted to usage as Lyapunov function for system with delay some quadratic Lyapunov functions constructed for ordinary differential system with limitation over its first derivative due to this system. The conditions of possibility of use of such quadratic functions as Lyapunov functions for delay system are presented.
Keywords: system with delay, stability, direct Lyapunov method, quadratic Lyapunov function. 
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O. G. Antonovskaya. Application of quadratic Lyapunov functions to investigation of stability  of systems with delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 15-20. http://geodesic.mathdoc.fr/item/IVM_2019_10_a1/

[1] Lyapunov A. M., Obschaya zadacha ob ustoichivosti dvizheniya, Izd-vo tekhn.-teor. lit., M.–L., 1950

[2] Barbashin E. A., Funktsii Lyapunova, Nauka, M., 1970

[3] Kim A. V., Pryamoi metod Lyapunova v teorii ustoichivosti sistem s posledeistviem, Izd-vo Ural. un-ta, Ekaterinburg, 1992

[4] Razumikhin B. S., Ustoichivost ereditarnykh sistem, Nauka, M., 1988 | MR

[5] Krasovskii N. N., “Ob asimptoticheskoi ustoichivosti sistem s posledeistviem”, Prikl. matem. i mekhan., 20:4 (1956), 513–518

[6] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Gostekhizdat, M., 1959

[7] Gorbunov A. V., Kamenetskii V. A., “Metod funktsii Lyapunova dlya postroeniya oblastei prityazheniya sistem s zapazdyvaniem”, Avtomatika i telemekhanika, 2005, no. 10, 42–53 | Zbl

[8] Razumikhin B. S., “Primenenie metoda Lyapunova k zadacham ustoichivosti sistem s zapazdyvaniem”, Avtomatika i telemekhanika, 21:6 (1960), 740–748 | Zbl

[9] Antonovskaya O. G., “O postroenii kvadratichnoi funktsii Lyapunova s zadannymi svoistvami”, Differents. uravneniya, 49:9 (2013), 1220–1224 | Zbl

[10] Antonovskaya O. G., “O vybore koeffitsientov kvadratichnoi funktsii Lyapunova s zadannymi svoistvami”, Differents. uravneniya, 52:3 (2016), 276–281 | MR

[11] Antonovskaya O. G., Goryunov V. I., “Ob odnom sposobe otsenki razmerov oblasti prityazheniya nepodvizhnoi tochki nelineinogo tochechnogo otobrazheniya proizvolnoi razmernosti”, Izv. vuzov. Matem., 2016, no. 12, 12–18 | MR | Zbl