On necessary assumptions in continuous time model reference adaptive control

An examination is made of the standard assumptions of model reference adaptive control (MRAC). The extent to which several of them are necessary is discussed. It is shown that in order to choose a reference model which is compatible with the plant: (i) an upper bound on the plant relative degree must be known in advance, (ii) the plant zeros on the imaginary axis must lie in a known finite set, and (iii) if the reference model input is not known to a sufficient extent in advance, then it is necessary that the plant zeros in the open right half-plane lie in a known finite set as well. These requirements are imposed by the problem and are controller independent