On a Lyapunov approach to stability analysis of 2-D digital filters

This paper describes an approach to the stability analysis of two-dimensional (2-D) digital filters that are modeled in the Fornashni-Marchesini state space using a class of generalized 2-D Lyapunov equations, the generalization was made based on the constant 2-D Lyapunov equation proposed recently by Hinamoto (see ibid., vol. 40, no. 2, p. 102-10, 1993). It is shown that the use of the generalized Lyapunov equations narrows the gap between “sufficiency” and “necessity” for a state-space digital filter to be stable, which occurs in Hinamoto´s Lyapunov theorem. Feasible methods for finding numerical solutions of the generalized 2-D Lyapunov equation are also proposed. An example is included to illustrate the main results of the paper