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 Nelin. Dinam., 2019, Volume 15, Number 3, Pages 309–326 (Mi nd662)

Mathematical problems of nonlinearity

Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom

S. D. Grilloa, L. M. Salomoneb, M. Zuccallib

a Instituto Balseiro, UNCuyo-CNEA, av. Bustillo 9500, San Carlos de Bariloche, Río Negro, República Argentina
b CMaLP, Fac. de Ciencias Exactas, UNLP, 50 y 115, La Plata, Buenos Aires, República Argentina

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.

Keywords: underactuated systems, Hamiltonian systems, asymptotic stability, Lyapunov functions

 Funding Agency Grant Number Consejo Nacional de Investigaciones Cientificas y Tecnicas S. D. Grillo and L.M. Salomone thank CONICET for its financial support.

DOI: https://doi.org/10.20537/nd190309

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MSC: 93D05, 93D20, 93C10
Accepted:12.09.2019

Citation: S. D. Grillo, L. M. Salomone, M. Zuccalli, “Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom”, Nelin. Dinam., 15:3 (2019), 309–326

Citation in format AMSBIB
\Bibitem{GriSalZuc19} \by S.~D.~Grillo, L.~M.~Salomone, M.~Zuccalli \paper Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom \jour Nelin. Dinam. \yr 2019 \vol 15 \issue 3 \pages 309--326 \mathnet{http://mi.mathnet.ru/nd662} \crossref{https://doi.org/10.20537/nd190309} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4021372} 

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