State feedback design for input-saturating quadratic systems

This paper proposes a method to design stabilizing state feedback control laws for nonlinear quadratic systems subject to input saturation. Based on a quadratic Lyapunov function, a modified sector condition and a particular representation for the quadratic terms, synthesis conditions in a “quasi”-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the state feedback gains maximizing the estimate of the stability region of the closed-loop system.