Enlarging region of attraction via LMI-based approach and Genetic Algorithm

In this paper, we consider the problem of the enlargement of the region of attraction of polynomial nonlinear systems. We use an optimization strategy based on Linear Matrix Inequality (LMI), to compute the region of attraction (RA). The main contribution consist in a preliminary estimation of the general form of this region obtained by the trajectory reversed Method. Moreover, an explicit determination of the RA by using a parameterized Lyapunov function is proposed. The parameters are computed by combining Genetic Algorithm and LMI. An example is given to illustrate the efficiency of the proposed approach.