Improving the Estimation of Region Attraction: A Case Study on Tumor Dormancy Equilibrium

This paper proposes a computational method to estimate the stability region of a locally asymptotically stable equilibrium point for polynomial nonlinear systems. In this method a local Lyapunov function is computed andthe region of attraction for the equilibrium point is estimated using one of its level sets. In this method, a subset of the level set is defined as the shape factor. Enlarging the shape factor inside the level set leads to a larger estimation of the region of attraction. Choosing the shape factor as well as the dynamic model of the system affects the shape and the size of the ROA estimation. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. To demonstrate the performance of the proposed method, we investigate a quadratic model of tumor growth using prey-predator system and estimate its ROA.