Asymptotic rejection of unmatched general periodic disturbances in a class of nonlinear systems

The study deals with asymptotic rejection of unmatched general periodic disturbances in nonlinear systems in the output feedback form. The class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form, 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. An equivalent input disturbance is introduced based on the periodic steady-state solutions of the system state variables. Conditions are identified for the existence of such an equivalent input disturbance. The half-period alternating feature is ensured for the equivalent input disturbance based on the fact that the steady state solutions of stable linear systems are shown to be half-period alternating if the inputs are. 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.