Asymptotic quotient observers for 2-D Fornasini Marchesini models

The concepts of conditioned-invariant, detectability and input-containing subspaces are developed within the context of observer design for 2-D Fornasini-Marchesini models in a general form. Specifically, a link is establised between these subspaces and the existence of so-called quotient observers, which estimate the local state modulo a conditioned invariant subspace. We also consider the synthesis of observers that are asymptotic in the sense that the estimation error (modulo a conditioned invariant subspace) tends to zero away from the boundary values.