Nonlinear feedback, double bracket dissipation and port control of Lie-Poisson systems

Methods from controlled Lagrangians, double bracket dissipation and interconnection and damping assignment – passivity based control (IDA-PBC) are used to construct nonlinear feedback controls which (asymptotically) stabilize previously unstable equilibria of Lie-Poisson Hamiltonian systems. The results are applied to find an asymptotically stabilizing control for the rotor driven satellite, and a stabilizing control for Hall magnetohydrodynamic flow.