Asymptotic Rejection of Disturbances with Asymmetric Wave Patterns in Output-feedback Nonlinear Systems

This paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns. This 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 systems considered in this paper can be transformed to the nonlinear output feedback form. The amplitude and phase of the disturbances are unknown. A new delay operator and the newly proposed half-period integration technique are used for estimation of the unknown disturbances in the systems, together with observer design techniques to deal with nonlinearity. The proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance, and ensures the overall stability of the system