In this paper, we propose designing method for separable-denominator two-dimensional Infinite Impulse Response (IIR) filters (separable 2D IIR filters) by Successive Projection (SP) methods using the stability criteria based on the system matrix. It is generally known that separable 2D IIR filters are stable if and only if each of the denominators is stable. Therefore, the stability criteria of 1D IIR filters can be used for separable 2D IIR filters. The stability criteria based on the system matrix are a necessary and sufficient condition to guarantee stability in 1D IIR filters. Therefore, separable 2D IIR filters obtained by the proposed design method have a smaller error ripple than those obtained by the conventional design method using the stability criterion of Rouche's theorem.

An extension is made for a set of systems that have a quadratic Lyapunov function in common for the purpose of analysis and design. The nominal set of system matrices comprises stable symmetric matricies, which admit a hyperspherical Lyapunov function. Based on stability robustness results, sets of matrices are constructed so that they share the same Lyapunov function with the nominal ones.