Disturbance estimator and its application in estimation of system output derivatives

A disturbance estimator is proposed for estimating unmeasurable disturbances which may be arbitrarily time-varying and/or grow to infinity with a cone-bounded growth rate. It is shown that estimation of the disturbance is achieved to any desired accuracy within a finite period of time. The idea behind the disturbance estimator is then applied to the estimation of output derivatives for uncertain linear systems. Under an assumption that the system input is a state feedback control with bounded feedback gains, the proposed scheme can estimate output derivatives up to the (r-1)st order, where r is the relative degree of the system. When r is larger than two, the proposed estimation scheme is first obtained in an unrealizable form, and then its approximation in a realizable form is suggested. The realizable scheme is verified to be effective by a computer simulation study