On exosubsets and internal models

Consideration is given to the internal model principle for linear multivariable regulators. The paper examines the possibility of directly constructing a suitable exosubset of regulator states from elementary dynamical descriptions of plant, exosystem, and controller on the basis of quotient set representation of exosystem states. It is found that exosubset existence is a nontrivial question; the importance of product vs coproduct state descriptions for the regulator is emphasized.