A novel strategy to enlarge the domain of attraction of affine nonlinear systems

In this paper, a novel strategy to enlarge the domain of attraction of an asymptotically stable, affine nonlinear system is proposed. This method is based on the concept of mapping and relies on asymptotic stability of a nonlinear system image via a continuous and injective mapping. The goal of designing the controller is to map the domain of attraction of an open loop system into a larger domain, which is the domain of attraction of a closed loop system. To find a suitable map that can make desired changes in the shape and size of domain of attraction, a criterion is obtained and its implementation instruction is described through examples. Simulation results are provided to demonstrate the efficiency of the proposed method.