Extended Observer Form for Nonlinear System with Disturbances: Algorithm and Application

The paper addresses the problem of transforming single-output nonlinear state equations affine in disturbance into an extended observer form whose nonlinear injection part depends additionally on the derivatives of the output up to a finite order. Moreover, the considered form is affine in disturbance. Based on the earlier results a detailed algorithm is given and applied to the model of a synchronous machine connected to an infinite bus. For the system in the extended observer form a reduced-order Kalman-filter based observer can be designed such that its error dynamics is exponentially attractive and it is stable in the input-to-state sense with respect to the disturbance.