Relative Degree and Invertibility

Invertibility of a dynamical system is important in left (input reconstruction) and right inversion (tracking control) problems. 

Role of relative degree is important in tracking control and input reconstruction problems as  well. The notion relative degree has subtleties and nuances in the case of multi-input, multi-output (MIMO) systems on account of different input-output delays.

The properties of invertibility and relative degree are closely-related and in fact, it can be shown that a system having well defined relative degree is invertible.