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A polynomial approach to nonlinear state feedback stabilization of saturated linear systems

The paper revisits the local exponential stabilization and global asymptotic stabilization problems of saturated linear systems using nonlinear control laws. The proposed approach takes advantage of a rational formulation of the control action in terms of a parameter σ, which is the solution to an implicit equation depending on the state, scheduling the control law. Constructive solutions are then proposed by considering sum-of-squares formulation of the conditions, when imposing a polynomial dependence on parameter σ.