The application of monotone stability to certain saturated feedback interconnections

Due to the conservatism of the conventional, or affine, small gain theorem, in some situations its use may not give an accurate indication of the true performance achievable in a given system. This is especially true of certain feedback loops with saturation elements present. Here, the recently derived monotone small gain theorem is discussed with respect to these types of system, and it is shown how certain constructions of feedback will guarantee global stability of the interconnection. This result is then applied to two instances where this type of configuration naturally occurs: anti-windup compensation and systems with “soft” output constraints