7. Conclusion

In this article, we discuss static anti-windup synthesis, which consists in modifying the previously synthesized controller only when actuator saturation is active. The proposed methods are based on the use of sector conditions to encapsulate the saturation function, and quadratic Lyapunov functions. This enables stability and performance conditions to be expressed in terms of linear matrix inequalities.

The disturbances considered were energy-bounded. Similar algorithms could be developed for amplitude-bounded disturbances. Furthermore, this article considers the case of control (stability of origin) and it is clear that the tracking problem is fundamental in many applications. Amplitude-bounded disturbances can thus be used to represent set-point changes. More generally, anti-windup synthesis techniques are already available in this context in the literature,...