Generalized sector synthesis of output feedback control with anti-windup structure

This paper considers the control synthesis problem for linear time invariant (LTI) continuous-time systems with actuator saturation nonlinearities. The control architecture is standard; a nominal LTI output feedback with an anti-windup (AW) mechanism. Traditional approaches have focused on AW synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the AW compensator is added to guarantee stability/performance properties when the actuators saturate. In contrast, this paper proposes a synthesis method to design both the nominal controller and the AW compensator simultaneously. Using the generalized sector (GS) approach in the multiplier setting, a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed-loop system. Our result is shown to include the existing results on the simultaneous circle synthesis and the anti-windup GS synthesis as special cases. This paper also shows that the direct feed-through term in the AW compensator does not contribute to enlarging the achievable domain of attraction within the multiplier GS framework.