An algorithm for robust stability of discrete systems

In many applications digital recursive filter coefficients have no distinct values, therefore the test of an entire family of polynomials is required in order to be sure of the filter stability. The edge theorem by Bartlett, Hollot and Lin states that a polytope is stable, if and only if, the exposed edges are stable. In this paper this last condition is transformed into an equivalent one that can be tested in a finite number of arithmetic operations and from which an algorithm is derived. It is shown that the condition, which has been established, is optimal i.e., it can neither be avoided, nor simplified.