Passivity and Passive Feedback Stabilization for a Class of Mixed Potential Systems

Abstract

This paper studies the input-output properties of a class of control affine systems where the drift dynamics is generated by a metriplectic structure. Those systems, related to generalized (or dissipative) Hamiltonian systems, are generated by a conserved component and a dissipative component and appear, for example, in non-equilibrium thermodynamics. In non-equilibrium thermodynamics, the two potentials generating the dynamics are interpreted as generalized energy and generalized entropy, respectively. In this note, passivity and passive feedback stabilization of this class of systems are studied, with the output function taken as the gradient of the conserved component of the dynamics, and the proposed storage function is computed using the dissipative (metric) component of the dynamics.