Easily testable sufficient conditions for the robust stability of systems with multilinear parameter dependence

A number of robust stability problems take the following form. A polynomial has real coefficients which are multilinear in real parameters that are confined to a rectangular axis-parallel box in parameter space. An efficient method is required for checking the stability of this set of polynomials. We present two sufficient conditions in this paper, which can be applied in many cases. They involve checking certain properties at the corners and edges of the parameter space box.