Observer Design Using Potential Based Realizations

This paper considers observer design for nonlinear dynamical systems which can be approximated by a dissipative Hamiltonian realization. The design approach decomposes the system associated one-form of a given dynamical system over an indeterminate metric using the Homotopy operator to generate exact (potential driven) and anti-exact parts. Then the convexity of the potential system given by the exact part is assessed and we propose a metric equation which yields a Lyapunov function for the potential driven observer system. An application of this method is demonstrated for a two-dimensional van der Pol oscillator.