Stability and feedback stabilization for a class of mixed potential systems

This paper studies the problems of stability analysis and feedback stabilization design for a class of control affine systems where the drift dynamics is generated by a metriplectic structure. Those systems are composed of a conserved part and a dissipative part and appear, for example, in non-equilibrium thermodynamics. They 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 constructing, by homotopy centered at an equilibrium of the system, a potential for the metriplectic system that can be used as a Lyapunov function candidate for the system, and in using the obtained potential to construct damping state feedback controllers. Stability of the closed-loop system is then considered.