Anti-windup for local stability of unstable plants

We consider the problem of anti-windup compensation based on coprime factorizations, for unstable plants with an input saturation nonlinearity. Firstly, we show that the behaviour of the compensated system is related to the behaviour of a simple linear system in feedback with a deadzone nonlinearity. We then state a local stability result which applies to such systems, and state under what conditions this result is non-trivial. For the anti-windup problem, we propose a low-order anti-windup compensator which is guaranteed to satisfy these conditions whenever possible, and hence provides some non-trivial level of local stability. This is illustrated by an example.