Global and local analysis of coprime factor-based anti-windup for stable and unstable plants

This paper considers analysis of anti-windup compensators based on coprime factorizations, for linear time-invariant plants with an input saturation nonlinearity. An explicit local L
2
gain bound is presented which relates the size of the external disturbances to the difference between signals in the saturated system and the corresponding signals in the nominal (unsaturated) system. This result shows how stability and performance degrade gracefully as the external disturbances grow larger, and also gives some intuition into how the local properties are determined by the H
∞
- and H
2
-norms of the system components.