Stability analysis of dynamical systems via R-functions

This paper provides a new method to estimate the Region of Asymptotic Stability (RAS) via computing the union of several regions, each one of them is known to be a subset of the RAS. The union is computed analytically by using R-functions, which represent a natural extension of Boolean functions to real-valued functions. The benefit of the proposed approach is that usually the best Lyapunov function to estimate the RAS is not known, but each trial of a different candidate Lyapunov function provides a subset of the RAS. Therefore R-functions can be used to compute the union of all the estimations, taking into account all the performed trials. Sufficient conditions for the union R-function to be a new composite Lyapunov function are provided, and performances of the proposed approach are tested over classic benchmark problems.