When is a model good for control design?

The use of an identified model for the design of a feedback controller for an actual plant introduces strictures on the quality of the model which are different from those pertaining in open loop identification. For example, a model Pˆ is admissible for the design of a controller for the actual plant P only if the pair (Pˆ, P) is simultaneously stabilizable. This paper addresses the question of the quality of a model to be used for control design, by analysing the interplay between the plant P, the designed closed loop system T and the set of admissible models {Pˆ}. For given P and T we characterize the set of admissible models {Pˆ}, where admissible means that a controller designed from Pˆ and T yields a stable closed loop. Necessary conditions on (P, T) are derived for this set to be nonempty