A fast algorithm for checking the stability of the convexcombination of stable polynomials

摘要

The approach to the stability of uncertain plants by means ofpolytopic polynomials often leads to a combinatorial explosion of thenumber of edges of a polytope whose stability has to be checked. Toreduce the computational burden of this combinatorial explosion to aminimum a fast algorithm for checking the stability of the edges of apolytope is proposed. The major computation involved is the solution ofthe positive real roots of two polynomials with degree less than orequal to