Geometric Construction of Mixed Potentials

This paper presents an approach to construct mixed potentials, to be used as storage functions in the context of dissipative systems theory. The objective is to obtain, through a locally-defined geometric decomposition of a given drift vector field, a potential similar to the thermodynamically-defined availability function proposed in the literature. The mixed potential is obtained by homotopy integration of a differential one-form for the drift vector field which decomposes the system into an exact part (generated by a potential) and an anti-exact part (which is not directly generated by a potential). The key element in the proposed approach is the computation of an integrating factor for the anti-exact part of the dynamics.