The Fornasini-Marchesini model with no overflow oscillations and its application to 2-D digital filter design

Based on a two-dimensional (2-D) local state-space (LSS) model that was proposed by E. Fornasini and G. Marchesini (Math. Syst. Theory, vol.12, p.59-72, 1978), a new condition for 2-D discrete systems to be asymptotically stable is introduced. This condition is more general than that based on the Roesser LSS model and includes the latter as a special case. A necessary and sufficient condition for 2-D discrete systems to be asymptotically stable is given in detail, without loss of generality. A criterion that sufficiently guarantees the absence of overflow oscillations in the Fornasini-Marchesini model is shown. The asymptotic stability condition is incorporated in the 2-D filter design