On the Robust Regulator for Linear Systems With Limited Parameter Uncertainty

The linear servomechanism problem has been studied for two extreme cases. On one extreme, the problem has been studied without considering the plant parameter uncertainty. On the other extreme, the problem has been studied for the worst parameter uncertainty in the sense that all the plant parameters are allowed to vary arbitrarily in the neighborhoods of their nominal values. Between these two extreme cases is what will be called limited uncertainty case where the entries of the plant matrices vary functionally with respect to some variables. This case will be studied in this paper. The main result is that, in the limited uncertainty case, the order of the robust regulator can be strictly less than the minimal order of the robust regulator with respect to the worst parameter uncertainty.