Feedback Stabilization of Metriplectic Systems

This paper considers the problem of stabilizing control affine systems where the drift dynamics is generated by a metriplectic structure. These systems can be viewed as an extension of generalized (or dissipative) Hamiltonian systems, where two potentials, interpreted as generalized energy and entropy, are generating the dynamics. The proposed approach consists in generating, by homotopy centered at an equilibrium of the system, a mixed potential for the metriplectic system, and in using the obtained potential to construct a damping state feedback controller. Stability of the closed-loop system is then considered.