Computing a Basin of Attraction to a Target Region by Solving Bilinear Semi-Definite Problems

In this paper, we present a sum of squares programming based method for computing a basin of attraction to a target region as large as possible by iteratively searching for Lyapunov-like functions. We start with the basic mathematical notions and show how attraction to a target region can be ensured by Lyapunov-like functions. Then, we present an initial framework for getting an increasing sequence of basins of attraction by iteratively computing Lyapunov-like functions. This framework can be realized by solving bilinear semi-definite problems based on sums of squares decomposition. We implement our algorithm and test it on some interesting examples. The computation results show the usefulness of our method.

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