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A stochastic approach for computing the domain of attraction without trajectory simulation
We present an approach for the numerical computation of the domain
of attraction of some asymptotically stable set for continuous-time autonomous
systems. It is based on a set-oriented approximation of the original
dynamical system by a Markov jump process. The domain of attraction is
extracted from absorption probabilities of the jump process. The method does
not perform any trajectory simulation, integrals of the underlying vector eld
on the boundary of partition elements are computed instead.