On the stability of periodic poincaré solutions of Hamiltonian systems in the degenerate case

1983 ◽  
Vol 47 (5) ◽  
pp. 594-600
Author(s):  
A.A. Saitbattalov
Keyword(s):  
Hamiltonian Systems ◽  
Degenerate Case ◽  
The Stability

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

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

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.

The stability domains of hamiltonian systems

1999 ◽  
Vol 63 (4) ◽  
pp. 545-555 ◽  
Author(s):  
A.A. Mailybaev ◽  
A.P. Seiranyan
Keyword(s):  
Hamiltonian Systems ◽  
The Stability

The stability of linear periodic Hamiltonian systems under non-Hamiltonian perturbations

1995 ◽  
Vol 59 (6) ◽  
pp. 829-836
Author(s):  
L.A Bondarenko ◽  
Ye.S Kirpichnikova ◽  
S.N Kirpichnikov
Keyword(s):  
Hamiltonian Systems ◽  
The Stability
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