Convex M-matrices and polytopic dynamic systems

The purpose of this paper is to derive a number of sufficient conditions for all matrices in a convex polytope to be M-matrices. The conditions involve only vertex matrices of the polytope and can be used to establish robust stability of systems with polytopic uncertainty structures. Applications of the convexity conditions will be made to uncertain linear constant systems and Lotka-Volterra population models. An interesting feature of the analysis is the use of Lyapunov functions which depend on systems parameters.