Stability and exponential stability of an adaptive control scheme for plants of any relative degree

Relying on a new adaptive pole assignment control scheme for plants with unknown relative degree and uncertain order which can be made minimum phase by means of a relative-degree-one first order parallel compensator, a new adaptation mechanism is proposed in this note in order to tackle with the problem of the attainment of an exponentially stable behavior of the output error. In particular, the connection between exponential stability and persistent excitation is outlined, and a complete stability analysis is performed