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 str ucture and the uncertain parameters are nonoverlapping, then the corre sponding value sets will be convex polygons. This means that the use o f the zero exclusion condition to test the robust stability of such un certain polynomials is feasible since we need only to calculate the ex treme points of the convex polygons. Furthermore, a version of the Edg e Theorem can be, used to test the robust stability of such uncertain polynomials.