×

zbMATH — the first resource for mathematics

Determination of the coefficients of a quadratic Lyapunov function with given properties. (English. Russian original) Zbl 1348.34100
Differ. Equ. 52, No. 3, 265-271 (2016); translation from Differ. Uravn. 52, No. 3, 275-281 (2016).
Summary: We discuss the possibility of choosing the coefficients of a quadratic Lyapunov function so as to ensure the sign negativeness of its first derivative (first difference) with a given margin.

MSC:
34D20 Stability of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lyapunov, A.M., Obshchaya zadacha ob ustoichivosti dvizheniya (General Problem of the Stability of Motion), Moscow-Leningrad: Gosudarstv. Izdat. Tekhn.-Teor. Lit., 1950. · Zbl 0041.32204
[2] Chetaev, N.G., Ustoichivost’ dvizheniya (Stability of Motion), Moscow: Nauka, 1966.
[3] Kosyakin, A.A. and Shamrikov, B.M., Kolebaniya v tsifrovykh avtomaticheskikh sistemakh (Oscillations in Digital Automated Systems), Moscow, 1983.
[4] Barbashin, E.A., Funktsii Lyapunova (Lyapunov Functions), Moscow, 1970. · Zbl 0206.37803
[5] Khusainov, D.Ya.; Yun’kova, E.A., A method of determining the solution of the Lyapunov equation with a given spectrum, Ukrain. Mat. Zh., 36, 528-531, (1984) · Zbl 0551.34029
[6] Sarybekov, R.A., Extremal quadratic Lyapunov functions of second order systems of equations, Sib. Mat. Zh., 18, 1159-1167, (1977) · Zbl 0386.34049
[7] Komarov, Yu.A.; Khusainov, D.Ya., Some remarks on the Lyapunov extremal function for linear systems, Ukrain. Mat. Zh., 35, 750-753, (1983) · Zbl 0549.34052
[8] Propoi, A.I., On the problem of the stability of motion, Avtomat. i Telemekh., 4, 51-60, (2000) · Zbl 1137.34339
[9] Antonovskaya, O.G., On the construction of a quadratic Lyapunov function with given properties, Differ. Uravn., 49, 1220-1224, (2013) · Zbl 1291.34093
[10] Antonovskaya, O.G., On the maximum restriction on the sign-negativity of the first derivative (first difference) of a quadratic Lyapunov function, Differ. Uravn., 39, 1562-1563, (2003) · Zbl 1065.93030
[11] Antonovskaya, O.G., Construction of quadratic Lyapunov functions that satisfy given constraints for continuous and discrete dynamical systems, Izv. Vyssh. Uchebn. Zaved. Mat., 2, 19-23, (2004) · Zbl 1208.93121
[12] Neimark, Yu.I., Method of point transformations in the theory of nonlinear oscillations, Izv. Vyssh. Uchebn. Zaved. Mat., 1, 41-66, (1958)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.