Linear Systems with Non-Actuator Saturation

Throughout the previous chapters, we have closely examined linear systems with saturating actuators in a systematic manner. We will conclude this book with some results on linear systems subject to non-actuator saturation. We will establish necessary and sufficient conditions under which a planar linear system under state saturation is globally asymptotically stable. Another result that we will present in this chapter is the design of a family of linear saturated output feedback laws that would semi-globally stabilize a class of linear systems. Here, the saturated output is a result of sensor saturation. In general, the effects, and hence the treatment, of sensor saturation are very different from those of actuator saturation and are far from being systematically studied. The result presented here is only a very special situation which happens to be dual to a special case of the result presented in Chapter 4 on actuator saturation. Even in this special case, the mechanism behind the feedback laws is completely different.t