Abstract
Based on the Fornasini-Marchesini local state-space (LSS) model which can imbed the Roesser LSS model in it, a technique is developed for the design of two-dimensional (2-D) recursive digital filters. This is by incorporating a 2-D Lyapunov stability condition for the Fornasini-Marchesini LSS model into the 2-D filter design. The 2-D filter is designed by solving an unconstrained optimization problem. The resulting filter is more advantageous in the synthesis of the optimal filter structure with minimum roundoff noise or minimum sensitivity since the 2-D equivalent transformation matrix is not block-diagonal, but general. In addition, the resulting filter always guarantees the absence of overflow oscillation as well as the stability. An example is given to illustrate the utility of the proposed technique.
