Non-Euclidean Contraction Theory for Monotone and Positive Systems

In this note we study contractivity of monotone systems and exponential convergence positive using non-Euclidean norms. We first introduce the notion conic matrix measure as a framework to stability systems. properties measures investigate their connection with weak pairings standard measures. Using pairings, characterize incremental respect Moreover, use provide sufficient conditions for equilibria. show that our leads novel results on (i) excitatory Hopfield neural networks, (ii) interconnected non-monotone comparison