A test of the stability of the two-dimensional recursive digital filter

An algorithm for testing the stability of a two-dimensional recursive digital filter is developed. The method tests a two-variable Hurwitz polynomial by using the theory of positive real functions. The stability conditions of a discrete system and a continuous system connected by a bilinear transformation for two variables are investigated. It is shown that the test of a two-variable Hurwitz polynomial reduces to a test of a Hurwitz polynomial of a lower order with respect to one variable and to a sign test of a real two-variable polynomial. The sign test is performed by Sturm's test extended for two-variables.