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Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances
Author(s) -
Polushin Ilya G.
Publication year - 2001
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.569
Subject(s) - torus , hamiltonian system , bounded function , mathematics , invariant (physics) , pure mathematics , hamiltonian (control theory) , lemma (botany) , control theory (sociology) , uniform boundedness , mathematical analysis , computer science , geometry , mathematical physics , mathematical optimization , control (management) , ecology , poaceae , artificial intelligence , biology
The problem of invariant tori stabilization in multi‐degrees‐of‐freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabilized. The estimates for region of attraction and ultimate bound are obtained. The essential role in the proof is played by Lemma 1, which gives the conditions for ultimate boundedness with respect to a given nonnegative smooth function V without assumption of negative (semi)‐definiteness of time derivative of V . Copyright © 2001 John Wiley & Sons, Ltd.