A Generalized Homotopy Operator Approach For Potential-Based Realization Of Nonlinear Systems

This paper proposes a generalized homotopy operator approach to decompose a given differentiable vector field and obtain a potential-based dynamic realization. The obtained representation is then exploited for stability analysis of nonlinear systems. In contrast to the standard homotopy decomposition approach built on a contraction of differential forms with respect to a fixed radial vector field, the generalized homotopy operator approach generates a potential minimizing residual terms in the decomposition from a weighted sum of convex potentials. The decomposition yields a realization of the vector field into dissipative and conservative components, and the potential generating the dissipative component is used for stability analysis of nonlinear dynamical systems.