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The family of limited model information designs, which construct controllers by accessing the plant's model in a constrained manner, is introduced in this paper. The closed-loop constant-disturbance rejection performance of the best Proportional-Integral (PI) controller that they can produce is investigated. For a class of linear discrete-time time-invariant plants, it is shown that there exists a limited model information control design which results in a PI controller whose closed-loop constant-disturbance rejection performance is in a bounded neighborhood of the optimal control design with full model information. This PI controller is the best PI controller that one can design under limited plant model information.
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