Asymptotic Rejection of Unmatched General Periodic Disturbances in Output-feedback Nonlinear Systems

This paper deals with asymptotic rejection of unmatched general periodic disturbances in nonlinear systems in the output feedback form. The system considered in this paper removes the restriction imposed on the asymptotic rejection of general disturbance in the literature that the disturbance only enters the system through the input channel. The class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form, some disturbances which are generated from nonlinear oscillation such as Van de Pol oscillators, as well as disturbances with symmetric half-period wave forms such as sinusoidal disturbances and triangular disturbances etc. The amplitude and phase of the disturbances are unknown. The steady state solutions of stable linear systems are shown to be half-period alternating if the inputs are. An equivalent input disturbance is then obtained through a partial state transform of the nonlinear system, and application of the results of the periodic solutions of stable linear systems to the zero-dynamics of the nonlinear system which are linear. With the equivalent input disturbances, the asymptotic rejection of unmatched general disturbances are converted to the matched cases. As the half-period alternating property is persevered in the equivalent input disturbances, recently proposed asymptotic rejection, based on the half-period integration and delay operations, of general periodic disturbances with asymmetric half-period wave forms can be applied, with a careful consideration of the phase offsets in the equivalent input disturbances. The proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance, and ensures the overall stability of the system.