A fast algorithm for checking the stability of the convex combination of stable polynomials

The approach to the stability of uncertain plants by means of polytopic polynomials often leads to a combinatorial explosion of the number of edges of a polytope whose stability has to be checked. To reduce the computational burden of this combinatorial explosion to a minimum a fast algorithm for checking the stability of the edges of a polytope is proposed. The major computation involved is the solution of the positive real roots of two polynomials with degree less than or equal to n/2 for each vertex. The computation required by the algorithm is mainly vertex dependent, and the burden of the combinatorial explosion of the number of edges is greatly reduced