This paper considers several explicit formulas for the construction of copositive Lyapunov functions for global asymptotic stability with respect to monotone systems evolving in either discrete or continuous time. Such monotone systems arise as comparison systems in the study of interconnected large-scale nominal systems. A copositive Lyapunov function for such a comparison system can then serve as prototype Lyapunov functions for the nominal system. We discuss several constructions from the literature in a unified framework and provide sufficiency criteria for the existence of such constructions.
19th International Symposium on Mathematical Theory Networks Systems (MTNS 2010). MTNS 2010: 19th International Symposium on Mathematical Theory Networks Systems. Proceedings (Budapest, Hungary 5-9 July, 2010)