Finding cones for K-cooperative systems
Provides a numerical tool for nonlinear system analysis, but the contribution is incremental as it applies existing theory to specific examples.
The paper develops a cone finding algorithm for analyzing nonlinear systems via differential positivity, enabling study of multi-stable systems beyond Lyapunov methods. The algorithm is demonstrated on a consensus problem with repulsive interactions and a controlled Duffing oscillator.
We design and test a cone finding algorithm to robustly address nonlinear system analysis through differential positivity. The approach provides a numerical tool to study multi-stable systems, beyond Lyapunov analysis. The theory is illustrated on two examples: a consensus problem with some repulsive interactions and second order agent dynamics, and a controlled duffing oscillator.