Asymptotic rejection of unmatched general periodic disturbances with nonlinear Lipschitz internal models

This article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with Lipschitz output nonlinearities for the internal model design. It is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions. Based on this observation, a nonlinear observer design with output Lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input-to-state stable zero dynamics. A number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear Lipschitz internal model can be applied. Two examples are included to demonstrate the proposed design strategies.