AN EFFICIENT ALGORITHM FOR CHECKING THE ROBUST STABILITY OF A POLYTOPE OF POLYNOMIALS

An efficient algorithm for checking the robust stability of a polytope of polynomials is proposed. This problem is equivalent to a zero exclusion condition at each frequency. It is shown that such a condition has to be checked at only a finite number of frequencies. We formulate this problem as a parametric linear program which can be solved by the Simplex procedure, with additional computations between steps consisting of polynomial evaluations and calculation of positive polynomial roots. Our algorithm requires a finite number of steps (corresponding to frequency checks) and in the important case when the polytope of parameters is a hypercube, this number is at most of order O(m3n2), where n is the degree of the polynomials in the family and m is the number of parameters.