An easily testable sufficient condition for the robust stability of multilinear uncertain polynomials

It has been shown in an earlier paper that for a class of multilinear uncertain polynomials, if a so-called intersection condition is satisfied, then the corresponding value sets will be convex polygons. In this paper, an easily testable sufficient condition for the robust stability of multilinear uncertain polynomials is given. This condition is equivalent to the intersection condition and easier to test. Also, we prove that this condition is preserved in a so-called preserving interval. With this property, we need only test a finite number of frequencies to check if the condition holds or not. Based on these results, a computer program is presented which tests the convexity of the value set.