Study of the BIBO stability of 2-D recursive digital filters in the presence of nonessential singularities of the second-kind-Analog approach

Since the work of Goodman, a pressing problem of research in multidimensional systems and circuits has been the study of nonessential singularities of the second type and testing for the bounded-input, bounded-output (BIBO) stability in the presence of those singularities. In this paper, the stability behavior of two-variable (2-V) analog functions in the presence of singularities of the second kind is studied. As the double bilinear transformation gives a unique mapping relationship between analog and digital biplanes, this study is aimed at contributing to the design of 2-D recursive filters based on 2-V analog circuit theory. Also, the relationship between the Hurwitz nature of the denominator of a 2-V function and BIBO stability is discussed.