On the Complete Instability of Interval Polynomials

In this paper, we study the "complete instability" of interval polynomials, which is the complement of classical robust Hurwitz stability. First, we state a necessary condition for stability which is used in the subsequent randomized algorithm. This algorithm has the objective to determine a stable polynomial in the interval family, if such polynomial exists. The second contribution of the paper is to provide new results for estimating the volume of stable polynomials. These results are based on a combination of deterministic and randomized methods. Finally, we present numerical examples and simulations showing the efficiency of the proposed methodology