TY - CONF AB - Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max-separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not. AU - Rantzer, Anders AU - Rüffer, Björn S. AU - Dirr, Gunther ID - 40778 T2 - Proc. 52nd IEEE Conf. Decis. Control TI - Separable Lyapunov functions for monotone systems ER -