Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions

Abstract

In this article a method is presented to find systematically the domain of attraction
\n(DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence
\nof special kind of Lyapunov functions Vn in a rational functional form approximating a
\nmaximal Lyapunov function VM that can be used to find an estimation for the DOA. Based
\non this idea, an improved method has been developed and implemented in a Mathematica-
\npackage to find such Lyapunov functions Vn for a class of hybrid (piecewise non-linear)
\nsystems, where the dynamics is continuous on the boundary of the different regimes in the
\nstate space.
\nIn addition, a computationally feasible method is proposed to estimate the DOA using
\na maximal fitting hypersphere.