Adaptive state regulation in the presence of disturbances of known frequency range

Adaptive state regulation via adaptive observation and asymptotic feedback matrix synthesis in the presence of bounded disturbances of known frequency range is considered. The adaptive observer uses a filtered output error to adapt parameter and state estimates. The filter is designed to attenuate in the disturbance frequency range. It is shown that, with persistent excitation, parameter errors are bounded by a quantity which is proportional directly to the attenuated disturbance magnitudes and inversely to the degree of persistent excitation. The accuracy of feedback gain estimates is shown to depend on these same quantities. Closed-loop stability is proven when the ratio of filtered disturbance magnitude to degree of persistent excitation is sufficiently small