Observer and dynamic feedback stabilizing control design for generalized Hamiltonian systems with unstructured dynamics

This paper considers the problem of dynamic output feedback controller design for the stabilization of systems described by the combination of a structured component, a generalized Hamiltonian system, and an unstructured dynamical component. First, a nonlinear Luenberger observer is designed for unmeasured state estimation. Then, using Lyapunov stability, a dynamic stabilizing feedback controller is designed. Asymptotic stability of the overall system in closed-loop is proven for systems centered at the origin and at an arbitrary output. Finally, application of the proposed approach is illustrated through numerical studies of a nonlinear chemical reactor system.