Analysis of L1L1 adaptive state feedback control. Why does it approximate an implementable LTI controller?

The analysis in this paper shows that L1L1 adaptive state feedback control approximates an implementable LTI controller because: (1) the addition of a low-pass filter in the controller structure leads to an internal loop in the controller and (2) high gain feedback within this loop leads to inversion of the linear reference model and cancellation of non-linear characteristics of the adaptation law. This result holds for a variety of adaptation laws and the achieved performance does not depend on the exact formulation of this law.