In this work, we address the problem of inner approximation of the maximal region of attraction set for continuous and discrete time polynomial systems. This problem is, in general, nonconvex and computationally hard. In this work, a semidefinite program based on the theory of measures and moments is provided which enables us to look for a Lyapunov function and associated region of attraction set. More precisely, for systems with polynomial dynamics, we first develop an infinite dimensional convex formulation over measure space to obtain Lyapunov function and approximate the maximal region of attraction set using the level set of this function. To solve this problem, a semidefinite program is provided, whose optimal solution is shown to converge to the solution of original problem. Problem Formulation: Equivalent Problem: Example: Papers:

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