Stability regions for linear systems with saturating controls via circle and Popov criteria

The problem of local stabilization of linear continuous-time systems subject to input saturation is addressed. The determination of stability regions for the saturated system is first considered via both the circle and Popov criteria. The absolute stability with a finite domain is thus studied from the resolution of some Riccati equations and quadratic optimization problems under linear constraints. Next, the synthesis of both state feedback controllers and stability domains is proposed via the use of linear matrix inequalities