Iterative method for estimating the robust domains of attraction of non-linear systems: Application to cancer chemotherapy model with parametric uncertainties

Abstract

In this paper, we present an iterative procedure method for estimating the robust domains of attraction of non-linear systems. This method is based on the approximation of the uncertain non-linear system with a parameters-dependent Convex Difference Inclusions (CDI) system and the classical iterative methods for linear systems, which are introduced in this paper. A robust one-step operator computing a sequence of convex sets is derived, and the polyhedral case is discussed. An algorithm summarizing the iterative procedure based on the robust one-step operator is given, which is the theoretical contribution of this paper. This method is applied to cancer chemotherapy model considering parametric uncertainties and it is shown that drastic reduction of the robust domain of attraction of the cancer chemotherapy model has happened and this is caused by the presence of parametric uncertainties. It is also proved that the aggressive chemotherapy is not the effective treatment for all the patients.