A behavioral approach to 2D estimation problems

Abstract—In this paper we address the dead-beat estimation problem for the class of two-dimensional (2D) behaviors which are described by means of a 2D difference equation, and whose trajectory evolutions pertain the “nonnegative half-plane”. For this class of behaviors, the concept of nilpotency is defined and fully characterized. After this preliminary step, the estimation problem is formally addressed. Indeed, the concept of 2D dead-beat observer (DBO) of the system relevant variables from the system measured variables is introduced, and a set of necessary and sufficient conditions for the existence of such a DBO is given. A complete parametrization of the family of all DBOs, together with a simple application of the theory here developed to the case of quarter-plane causal 2D state space models, conclude the paper.