Convexity in coefficient space for a class of multilinear uncertain polynomials

This paper considers a class of multilinear uncertain polynomials which defines a convex polytope in coefficient space. The main result is as follows: Suppose a multilinear uncertain polynomial has a symmetric uncertainty structure and the uncertainty box satisfies a non-overlapping assumption. If the dimension of the uncertainty box is greater than the dimension of the coefficient space, then the image of this uncertainty box will be a convex polytope in coefficient space. This result can be used in a robust pole placement problem in which complex closed loop poles are allowed