NP-hardness of polytope M-matrix testing and related problems
  In this note we prove NP-hardness of the following problem: Given a set of matrices, is there a convex combination of those that is a nonsingular M-matrix? Via known characterizations of M-matrices, our result establishes NP-hardness of several fundamental problems in systems analysis and control, such as testing the instability of an uncertain dynamical system, and minimizing the spectral radius of an affine matrix function. 
Nikos Vlassis
math.OC cs.CC cs.SY math.DS