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.

Kadam, S. D. and Palanthandalam-Madapusi, H.J., 2022, “A Note on Invertibility and Relative Degree of MIMO LTI Systems”. IFAC Journal of Systems and Control

Prof. Harish's post about the paper on LinkedIn with interesting details of the paper:

Harish Palanthandalam-Madapusi on LinkedIn: Basic System Properties - Discrete-Time MIMO SystemsThe most fun manuscript we have written in recent times, titled “A Note on Invertibility and Relative Degree of MIMO LTI Systems”, is now accepted for ...