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.

##### MSC:

70K20 | Stability for nonlinear problems in mechanics |

34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |

93D30 | Lyapunov and storage functions |

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\textit{A. A. Martynyuk} et al., Int. Appl. Mech. 54, No. 3, 346--357 (2018; Zbl 1397.70031); translation from Prikl. Mekh., Kiev 54, No. 3, 114--126 (2018)

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##### References:

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