Optimal design of IIR digital filters with robust stability using conic quadratic programming

In this paper, minimax design of infinite-impulse-response (IIR) filters with prescribed stability margin is formulated as a conic quadratic programming (CQP) problem. CQP is known as a class of well-structured convex programming problems for which efficient interior-point solvers are available. By considering factorized denominators, the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the IIR filter to have a prescribed stability margin. Also included in the formulation is a second-order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design and eliminates a line-search step. Collectively, these features lead to improved designs relative to several established methods.