Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances

Corresponding Author

Ilya G. Polushin

[email protected]

Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy, V.O., St. Petersburg, 199178, Russia

Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy, V.O., St. Petersburg 199178, Russia===Search for more papers by this author

Ilya G. Polushin,

Corresponding Author

Ilya G. Polushin

[email protected]

Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy, V.O., St. Petersburg, 199178, Russia

Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy, V.O., St. Petersburg 199178, Russia===Search for more papers by this author

First published: 06 March 2001

https://doi.org/10.1002/rnc.569

Citations: 3

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Abstract

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.

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Volume11, Issue3

Special Issue:Control of Oscillatory Systems

March 2001

Pages 253-265

Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances

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Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances

Abstract

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