Some new results on stability and stability robustness of Fornasini-Marchesini state-space 2-D digital filters

The paper describes a Lyapunov approach to stability and stability robustness analysis for 2D digital filters in the Fornasini-Marchesini local state-space setting (E. Fornasini and G. Marchesini, 1980). A class of new constant 2D Lyapunov equations, that generalize the 2D Lyapunov equation proposed recently by T. Hinamoto (1993), is described. It is shown that the generalized 2D Lyapunov equation can be used to derive a new stability condition that narrows the gap between the “necessity” and “sufficiency” that occurs in Hinamoto´s stability theorem. The generalized 2D Lyapunov equations are then utilized to derive two lower bounds of unstructured, stable perturbations of a given stable filter. Numerical techniques for solving the proposed 2D Lyapunov equations are also presented