Integral controllability and integrity for uncertain systems

It is well known that the relative gain array (RGA) and the determinant of the gain matrix provide useful information about integral controllability and integrity (e.g., failure tolerance), which are important issues in decentralized control. The RGA also gives information about robustness with respect to modeling errors and input uncertainty. Almost exclusively only nominal models have been considered in previous studies and applications of these methods. Not until recently have there been attempts to consider model uncertainty more explicitly. However, the methods proposed in these studies tend to find uncertainty bounds that are too wide. In this paper a more accurate procedure based on sensitivity analysis is developed for studying the effect of model errors. Independent gain uncertainty as well as more structured uncertainty can be handled. The method is well suited for deriving tight bounds on the tolerable uncertainty.