Matched Disturbance Rejection for Port-Hamiltonian Systems with Coupled Dynamics

Abstract

This paper investigates the rejection of matched disturbances generated by coupled port-Hamiltonian (PH) dynamics in previously stabilized PH systems. The disturbance dynamics are incorporated into a unified PH representation, allowing the disturbance to affect the plant through both the matched input channel and an interconnection structure. Unlike existing results that typically impose restrictive structures on the disturbance dynamics, the proposed framework accommodates a more general class of coupled PH disturbances, including nonzero interconnection and damping terms. A baseline disturbance rejection scheme is first established for known disturbance storage parameters. The framework is then extended to the case of an unknown symmetric storage matrix through online parameter estimation. Two control designs are developed under different structural conditions, with the latter relaxing the dimensional restriction imposed by the first design. The proposed methods guarantee asymptotic convergence of the plant state to the desired equilibrium, while preserving a port-Hamiltonian representation of the closed-loop dynamics under the corresponding conditions. The results generalize existing disturbance rejection approaches and broaden their applicability to coupled PH disturbance models.