Spatial-domain 2-D filter design using the Fornasini-Marchesini second model

A two-dimensional (2-D) Lyapunov equation with constant coefficients is considered for the Fornasini-Marchesini (FM) second local state-space (LSS) model. First, a condition is given that sufficiently guarantees the asymptotic stability. A technique is then developed in the spatial domain for the design of 2-D state-space digital filters with guaranteed asymptotic stability. This is done by incorporating the above stability condition into the 2-D filter structure. A numerical example is solved to illustrate the utility of the proposed technique.<>