Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

[+] Author and Article Information
S. N. Singh

Depto. de Engenharia Eléctrica, Universidade Federal de Santa Catarina, 88.000 - Florianópolis, SC, Brazil

J. Dyn. Sys., Meas., Control 104(1), 27-32 (Mar 01, 1982) (6 pages) doi:10.1115/1.3149627 History: Received February 03, 1981; Online July 21, 2009


Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

Copyright © 1982 by ASME
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