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.