BIBO stability in the presence of nonessential singularities of the second kind in 2-D digital filters
Leonid M. Roytman, M.N.S. Swamy, Gernot Eichmann · IEEE Transactions on Circuits and Systems · 1987
In this paper, the open problem regarding the BIBO stability of two-dimensional linear shift invariant filters, in the presence of nonessential singularities of the second kind, is considered. Necessary and sufficient conditions for boundedness, andl_2andl_1stabilities of a functionG(z_1, z_2)= P(z_1, z_2)/[Q(z_1, z_2)]^n, whereP/Qhas simple nonessential singularities of the second kind onT^2, are obtained. These conditions are expressed in a very simple way in terms of the multiplicity of the zeros of certain resultants of two-variable polynomials. Many illustrative examples are also given.