Path-Based Stability Analysis for Monotone Control Systems on Proper Cones

In this article, we study positive invariance and attractivity properties for nonlinear control systems, which are monotone with respect to proper cones. Monotonicity simplifies such analysis for specific sets defined by the proper cones. Instead of Lyapunov functions, a pair of so-called paths in the state space and input space play important roles. As applications, our results are utilized for analysis of asymptotic stability and also input-to-state stability on proper cones. The results are illustrated by means of examples.