Stabilizability of Controlled Lagrangian Systems of Two Degrees of Freedom and One Degree of Under-Actuation by the Energy-Shaping Method

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We provide some criteria for stabilizability by the energy-shaping method for the class of all controlled Lagrangian systems of two degrees of freedom and one degree of under-actuation: a necessary and sufficient condition for Lyapunov stabilizability, two sufficient conditions for asymptotic stabilizability, and a necessary and sufficient condition for exponential stabilizability. As a corollary, we show that some of the asymptotically stabilizing controllers that were designed in old literatures with the energy-shaping method are actually exponentially stabilizing controllers. Examples of such systems are the inverted pendulum on a cart, the Furuta pendulum, the ball and beam system, and the Pendubot.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2010-08
Language
English
Article Type
Article
Keywords

MECHANICAL SYSTEMS; STABILIZATION

Citation

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, v.55, no.8, pp.1888 - 1893

ISSN
0018-9286
DOI
10.1109/TAC.2010.2049279
URI
http://hdl.handle.net/10203/220793
Appears in Collection
EE-Journal Papers(저널논문)
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