A Construction of Strict Lyapunov Functions for A Bilinear Balancing Model ?

摘要

This paper focuses on a two-dimensional compartmental model which is linear except for bilinear terms of balancing kinetics. It is an equation of Lotka-Volterra type, but its structure is not symmetric like the predator-prey equation. This paper elucidates fundamental challenges in non-local stability analysis of the model. In particular, obstacles in constructing strict Lyapunov functions are discussed. A method consisting of tilting and semi-global construction is presented to overcome the challenges. Its benefit is highlighted from the viewpoint of input-to-state stability with respect to inflow perturbation.