Nonlinear Static State Feedback for Saturated Linear Plants via a Polynomial Approach

The technical note revisits the local exponential stabilization and global asymptotic stabilization problems of saturated linear systems using nonlinear control laws. The proposed nonlinear control law has rational dependence on a parameter σ, which is computed by solving an implicit equation depending on the state. Constructive solutions are obtained, based on a sum-of-squares formulation of the proposed conditions.