An immittance-type stability test for 2-D digital filters

The paper presents a `tabular´ stability test for 2-D linear shift invariant systems that is based on the stability test for 1-D discrete-time system polynomials introduced by Bistritz. The algorithm involves simple manipulations of 1-D and 2-D polynomial functions or corresponding and equivalent manipulations of vectors and matrices. The total computation cost is of order n⁶ (for a polynomial with variables of degrees are n1=n2=n) compared to typical costs that grow exponentially with n for previously reported 2-D tabular tests. The set of necessary and sufficient conditions for 2-D stability involves testing stability of a 1-D polynomial of degree n and testing positivity on an interval of a polynomial of degree 2n²