Estimation of Isostables and Basins of Attraction of Monotone Systems

Aivar Sootla, Alexandre Mauroy

Published 2015-10-05Version 1

In this paper, we study spectral properties of the so-called monotone systems and link these results with the celebrated Perron-Frobenius theorem for linear positive systems. Using these spectral properties we study the geometry of basins of attraction of monotone systems. Additionally, we show that under certain conditions we can bound the variations in these basins under parametric uncertainty in the vector field. We also provide a computational algorithm to estimate the basins of attraction and illustrate the results on two and three state monotone systems.