Geodesic
Stability Analysis Based on Nonlinear Inhomogeneous Approximation
Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 803-820

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The asymptotic stability of zero solutions for essentially nonlinear systems of differential equations in triangular inhomogeneous approximation is studied. Conditions under which perturbations do not affect the asymptotic stability of the zero solution are determined by using the direct Lyapunov method. Stability criteria are stated in the form of inequalities between perturbation orders and the orders of homogeneity of functions involved in the nonlinear approximation system under consideration.
Keywords: asymptotic stability, Lyapunov function, nonlinear approximation, cascade system, homogeneous function. 
@article{MZM_2011_90_6_a0,
     author = {A. Yu. Aleksandrov and A. V. Platonov},
     title = {Stability {Analysis} {Based} on {Nonlinear} {Inhomogeneous} {Approximation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--820},
     publisher = {mathdoc},
     volume = {90},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a0/}
}
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A. Yu. Aleksandrov; A. V. Platonov. Stability Analysis Based on Nonlinear Inhomogeneous Approximation. Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 803-820. http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a0/