Estimation of the Domain of Attraction of Free Tumor Equilibrium Point for Perturbed Tumor Immunotherapy Model

Abstract

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We find a specific Lyapunov function in order to vanish maximum perturbation of modeling error, aging or uncertainties which exist in this system. Using this method and appropriate Lyapunov function, we demonstrate that there is an invariant polytope that for the set of perturbed initial conditions belonging to such region, the convergence to the healthy state is guaranteed.

Keywords

• nonlinear system
• equilibrium point, stability
• domain of attraction
• lmi, lyapunov function
• perturbation
• tumor-free equilibrium point