An algorithm to transform discrete-time state equations into the extended observer form

Abstract

The problem of transforming a single-input single-output nonlinear discrete-time state equations into the extended observer form is studied in this paper. Unlike previous solutions which compute the injection terms from the input–output equations, in this paper the computations utilize directly the given state equations. An algorithm is given to find step-by-step the necessary transformation by computing backward-shifts of functions computed in previous step. It is shown that the integrability conditions presented in the algorithm are necessary and sufficient for solvability of the problem. Various examples have been studied to demonstrate the usefulness of the algorithm.