A class of multilinear uncertain polynomials to which the Edge theorem is applicable

This paper gives a class of multilinear uncertain polynomials to which the Edge theorem is applicable. In the paper, a notion of “symmetric uncertainty structure” is introduced. The main result is as follows: if a multilinear uncertain polynomial has a symmetric uncertainty structure and the uncertain parameters are non-negative and non-overlapping, then the corresponding value sets will be convex polygons. From this, it follows that a version of the Edge theorem can be used to test robust stability