On prediction-type reduced-order observers for discrete-time systems

Abstract

We define the combination of the standard reduced-order observer with one-step-ahead state predictor as the prediction-type reduced-order observer. We first obtain a simple and significant relation that ensures the equivalence of the reduced and the full-order observers in the steady state. We show the fact that a prediction-type reduced-order does not always provide a reduced-order controller. We also discuss the implications of the equivalence of the observers on state-space representation of the doubly-coprime factorization and YJB parametrization. We use the equivalence relation to clarify the feedback properties achieved by the loop transfer recovery technique using the prediction-type reduced-order observer at both the input and output of a square and minimum phase plant. In addition, we discuss the computational requirements for the observer-based controllers.