Geodesic
On stability of the inverted pendulum motion with a~vibrating suspension point
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 39-50

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Under study is the stability of the inverted pendulum motion whose suspension point vibrates according to a sinusoidal law along a straight line having a small angle with the vertical. Formulating and using the contracting mapping principle and the criterion of asymptotic stability in terms of solvability of a special boundary value problem for the Lyapunov differential equation, we prove that the pendulum performs stable periodic movements under sufficiently small amplitude of oscillations of the suspension point and sufficiently high frequency of oscillations.
Keywords: inverted pendulum, asymptotic stability, Lyapunov differential equation, contracting mapping principle. 
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     author = {G. V. Demidenko and A. V. Dulepova},
     title = {On stability of the inverted pendulum motion with a~vibrating suspension point},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     publisher = {mathdoc},
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     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a3/}
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G. V. Demidenko; A. V. Dulepova. On stability of the inverted pendulum motion with a~vibrating suspension point. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 39-50. http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a3/