Generalized Luenberger observers for 2D state-space models

In this paper the definition of generalized Luenberger observer (GLO) for a two-dimensional state-space model, described by the Fornasini-Marchesini model, is introduced. It is shown that reconstructibility is a necessary and sufficient condition for the existence of a dead-beat GLO. This proves that if a standard dead-beat observer exists, then, in particular, a dead-beat GLO can be found. A constructive algorithm for designing a dead-beat GLO is described, and two examples illustrate the design procedure and compare the performances, in terms of complexity, obtained by resorting to this class of observers with respect to the whole class of dead-beat observers.