Estimation of the Domain of Attraction of Equilibrium Points for Quadratic Systems: Application to Tumor Stability Analysis

This paper considers the following problem: given an asymptotically stable equilibrium point of a nonlinear quadratic system, determine whether an assigned polytope surrounding the equilibrium point belongs to its domain of attraction. The proposed algorithm requires the solution of a feasibility problem that can be casted in terms of linear matrix inequalities constraints. In view of the important role played by quadratic models in systems biology, the work focuses on the application of the proposed technique for a quantitative study of the development of tumor phenomena in human beings.