A stability theorem with applications to adaptive control

A theorem for the global asymptotic stability of a class of feedback systems is established. It is shown that the equivalent feedback representation of the equation associated with the generalized error of the model reference adaptive system (MRAS) belongs to this class. A general form of the parameter adaptation algorithm which contains as particular forms various known adaptation algorithma is introduced. Explicit stability conditions are obtained for the case of this general type algorithm. The usefulness of the results is illustrated by their application to the straightforward generalization of some recent MRAS designs.