This paper reviews the static output feedback problem in the control of linear, time-invariant LTI systems. It includes analytical and computational methods and presents in a uni ed fashion, the knowledge gained in the decades of research i n to this most important problem.

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In this paper, we seek to provide a systematic anti-windup control synthesis approach for systems with actuator saturation within a linear parameter-varying (LPV) design framework. The closed-loop induced L 2 gain control problem is considered. Di erent from conventional two-step anti-windup design approaches, the proposed scheme directly utilizes saturation indicator parameters to schedule accordingly the parameter-varying controller. Hence, the synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved very e ciently. The resulting gain-scheduled controller is non-linear in general and would lead to graceful performance degradation in the presence of actuator saturation non-linearities and linear performance recovery. An aircraft longitudinal dynamics control problem with two input saturation non-linearities is used to demonstrate the e ectiveness of the proposed LPV anti-windup scheme.

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