Reduced-order nonlinear discrete-time observer design using functional equations

The present research work proposes a new approach to the reduced-order nonlinear discrete-time observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer, the proposed approach develops a nonlinear analogue. The formulation of the reduced-order nonlinear discrete-time observer design problem is realized via a system of first-order linear nonhomogeneous functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory. The solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package. Copyright (C) 2001 IFAC.