Positivity and stability tests for multidimensional filters (discrete-continuous)

In this paper, a systematic procedure to test for stability of three-dimensional filters (discrete and continuous) is presented. The test is based on repeated applications of an extended Hermite or Schur-Cohn formulation, and use of Sturm's theorem to determine the content of a system of polynomial inequalities in a single indeterminate. The need for generating a constructive algorithm for stability tests for higher than three-dimensional filters using Tarski's generalization of Sturm's theorem is discussed. Application of certain combinatorial rules for transforming the multidimensional digital filter problem to the multidimensional continuous filter problem or vice versa) is made.