Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure

This correspondence is concerned with an image f(B^m) of a box B^m⊂R^m under a multiaffine transformation f:R^m→C. The authors introduce a notion of a principal point of B^m and prove that the boundary of f(B^m) is covered by images of principal points. The authors exploit this result to provide necessary and sufficient robust stability conditions for polynomials whose coefficients are multiaffine functions of parameters. An application of the general criterion obtained in the correspondence to the particular case of systems with a cascade of first-order uncertain blocks leads to a computationally tractable procedure that verifies stability of the systems