New techniques for constructing asymptotic stability regions for nonlinear systems

The paper deals with the problem of the estimation of regions of asymptotic stability for continuous, autonomous, nonlinear systems. After an outline of the main approaches available in the literature, the "trajectory reversing method" is presented as a. powerful numerical technique for low order systems. Then, an analytical procedure based on the same topological approach is developed, and a comparison is made with the classical Zubov method, noting the possibility of overcoming some of the classical method\´s drawbacks (e.g., its nonuniform convergence). Several examples of applications of the "trajectory reversing method" both in the numerical and analytical formulation are reported.