Relaxing PWQ Lyapunov stability criteria for PWA systems

Automatica ◽  
2013 ◽  
Vol 49 (2) ◽  
pp. 667-670 ◽  
Author(s):  
Morten Hovd ◽  
Sorin Olaru
Keyword(s):  
Lyapunov Stability ◽  
Stability Criteria ◽  
Lyapunov Stability Criteria

Justifying the Stabilization of a Marginally Stable Ship

2017 ◽  
Author(s):  
David Shekhtman ◽  
Dirk M. Luchtenburg
Keyword(s):  
Energy Dissipation ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Marginal Stability ◽  
Stability Conditions ◽  
Stability Criteria ◽  
Benchmark Problem ◽  
Zero Energy ◽  
External Disturbances ◽  
Lyapunov Stability Criteria

As a precursor to capsize, marginal stability, resulting from incorrect loading conditions and crew negligence, poses a serious danger to ships. Therefore, as a benchmark problem for preventing capsize, the use of an actively controlled pendulum for the stabilization of a marginally stable ship was analyzed. Lyapunov stability criteria and closed loop eigenvalues were used to evaluate the extent to which a proposed pendulum controller could cope with different ship stability conditions. Equations of motion were solved to observe the controller’s performance under different damping conditions. The behavior of the controller yielded the following results: a marginally stable ship can be stabilized, as long as there is no right hand plane zero; energy dissipation is key to the stabilization of a marginally stable ship; the controller must have knowledge of the ship’s stability to prevent controller-induced excitation; and a stabilized tilted ship is more robust to external disturbances than a stabilized upright ship.

Stochasticity of Galactic Orbits of Star Clusters

2015 ◽  
Vol 24 (2) ◽  
Author(s):  
L. V. Smirnova
Keyword(s):  
Lyapunov Exponents ◽  
Lyapunov Stability ◽  
Stability Criterion ◽  
Star Clusters ◽  
Open Clusters ◽  
Stability Criteria ◽  
Poincaré Sections ◽  
Lyapunov Stability Criterion ◽  
Poincare Sections

AbstractThe Lyapunov, Lagrange and Poincaré criteria are tested for orbits of 461 open clusters in an axisymmetric potential. Lyapunov exponents and Poincaré sections are computed, and all of the trajectories are found to be stable according to the Lagrange and Poincaré stability criteria. At the same time, some trajectories appear to exhibit minor instability according to the Lyapunov stability criterion.

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