Estimating the robust domain of attraction and directional enlargement of attraction domain via Markov models

This paper proposes a new approach for estimating the robust domain of attraction (RDA) and directional enlargement of the DA for dynamical systems. The proposed method analyzes stability of dynamical systems by Markov modeling and employs invariant measure as the stability indicator. Markov chains analysis focuses on asymptotic behaviors of systems and ignores the transient ones. The proposed method expresses the problem of estimating RDA and directional enlargement of DA as an infinite dimensional linear problem. The resulting linear problem is converted to a finite dimensional optimization problem using approximated Markov transition function. As a novel application, the directional enlargement of DA is used in order to increase the critical clearing time of power systems. The efficiency of proposed methods is shown via simulations.