Design of stable 2D IIR digital filters using iterative semidefinite programming

Semidefinite programming (SDP) has recently attracted a great deal of research interest. Among other things, the optimization tool was proven to be applicable to design various types of FIR digital filters. This paper describes an attempt on extending the SDP approach to 2-D IIR filters. It is shown that a stable 2-D IIR filter design in the minimax sense can be formulated as an iterative SDP problem. Stability constraints are expressed as linear matrix inequalities which fit nicely into the SDP-based design setting. Unlike the 1-D case, an alternating iteration scheme is used to deal with parameter nonlinearity encountered in the separable denominator polynomials. A design example is presented to illustrate the proposed method