Abstract:
For an underactuated (simple) Hamiltonian system with two degrees of freedom and one degree of underactuation, a rather general condition that ensures its stabilizability, by means of the existence of a (simple) Lyapunov function, was found in a recent paper by D.E. Chang within the context of the energy shaping method. Also, in the same paper, some additional assumptions were presented in order to ensure also asymptotic stabilizability. In this paper we extend these results by showing that the above-mentioned condition is not only sufficient, but also necessary. And, more importantly, we show that no additional assumption is needed to ensure asymptotic stabilizability.
Citation:
S. D. Grillo, L. M. Salomone, M. Zuccalli, “Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom”, Rus. J. Nonlin. Dyn., 15:3 (2019), 309–326
\Bibitem{GriSalZuc19}
\by S.~D.~Grillo, L.~M.~Salomone, M.~Zuccalli
\paper Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom
\jour Rus. J. Nonlin. Dyn.
\yr 2019
\vol 15
\issue 3
\pages 309--326
\mathnet{http://mi.mathnet.ru/nd662}
\crossref{https://doi.org/10.20537/nd190309}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4021372}
Linking options:
https://www.mathnet.ru/eng/nd662
https://www.mathnet.ru/eng/nd/v15/i3/p309
This publication is cited in the following 1 articles:
Sergio Grillo, Leandro Salomone, Marcela Zuccalli, “Explicit solutions of the kinetic and potential matching conditions of the energy shaping method”, JGM, 13:4 (2021), 629
Citation in format AMSBIB
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