A lower bound on the multivariable stability margin via linear programming

Consideration is given to the problem of robustness analysis in linear, time-invariant feedback systems with parametric uncertainty. It is shown that the distance from the origin of the image of an n-dimensional hypercube by a complex multilinear function can be formulated as a linear problem of complexity linearly proportional to the number of variables and nonlinear terms in the multilinear function. This approach gives, under certain reasonable conditions, a polynomial time algorithm in n to compute the multivariable stability margin