Justifying the Stabilization of a Marginally Stable Ship

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.

GLOBALLY EXPONENTIAL HYPERCHAOS (LAG) SYNCHRONIZATION IN A FAMILY OF MODIFIED HYPERCHAOTIC RÖSSLER SYSTEMS

In this paper, we consider a new family of modified hyperchaotic Rössler systems, recently studied by Nikolov and Clodong using proper nonlinear feedback controllers. Particular attention is given to (i) globally exponential lag synchronization (GELS) for τ > 0; and (ii) globally exponential synchronization (GES) for τ = 0. As a representative example, one system of the family of modified hyperchaotic Rössler systems is particularly studied, and Lyapunov stability criteria for the GELS and GES are derived via eight families of proper nonlinear feedback controllers. Moreover, we also present some nonlinear feedback control laws for other modified hyperchaotic Rössler systems. Numerical simulations are used to illustrate the theoretical results.