zbMATH — the first resource for mathematics

Constructive estimation of the Lyapunov function for quadratic nonlinear systems. (English. Russian original) Zbl 1397.70031
Int. Appl. Mech. 54, No. 3, 346-357 (2018); translation from Prikl. Mekh., Kiev 54, No. 3, 114-126 (2018).
Summary: A system of perturbed equations of motion with quadratic nonlinearity is considered. New estimates of the Lyapunov function are established and two conclusions are formulated. New motion constraints are presented. For two coupled systems of equations, boundedness conditions for some of the variables are established. Practical motion constraints in given domains of initial and subsequent perturbations are established. A system of quasi-linear equations is considered as an example.

70K20 Stability for nonlinear problems in mechanics
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
93D30 Lyapunov and storage functions
Full Text: DOI
[1] A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, London (1992). · Zbl 0786.70001
[2] A. A. Martynyuk and R. Gutowski, Integral Inequalities and Stability of Motion [in Russian], Naukova Dumka, Kyiv (1979).
[3] D. Ya. Khusainov, I. A. Dzhalladova, and O. a. Shatirko, “Estimating the stability domain of a differential system with a quadratic right-hand side,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, 3, 227-230 (2011). · Zbl 1249.34150
[4] Martynyuk, AA, Novel bounds for solutions of nonlinear differential equations, Appl. Math., 6, 182-194, (2015)
[5] Martynyuk, AA; Khusainov, DY; Chernienko, VA, Integral estimates of solutions to nonlinear systems and their applications, Nonlin. Dynam. Syst. Theor., 16, 1-11, (2016) · Zbl 1343.34131
[6] B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, Boston (1997). · Zbl 0879.34013
[7] T. Yoshizawa, Stability Theory by Liapunov’s Second Method, The Math. Soc. of Japan, Tokyo (1966).
[8] T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer, Berlin (1975). · Zbl 0304.34051
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.