Polynomial level-set methods for nonlinear dynamical systems analysis

In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. The problem of flowing these sets under the advection map of a dynamical system is converted to a semidefinite program, which we use to compute the coefficients of the polynomials. We further address the related problems of constraining the degree of the polynomials and the connectedness of the associated sets.