This paper focus on the problem of estimating the region of attraction of nonlinear control systems that can be put in a rational algebraic-differential form. The estimates are computed by means of invariant domains associated to rational Lyapunov functions. The saturation effects are taken into account by the use of a generalized sector condition for deadzone nonlinearities. These ingredients lead to the formulation of an LMI-optimization problem for computing regions of stability for the closed-loop system.
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